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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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In this video, we're going to talk about analog versus digital. Something that's analog can be any value within a given range, while something digital is represented by a number of discrete or separate levels. To distinguish these two ideas, I like to think about clocks. An analog clock has the numbers in the hands, and it's analog because the motion of those hands is continuous. They can sweep across the circle, representing any of infinite times on that clock. For example, between 3.06 and 3.07, the minute hand is actually going to be at some point between those marks on the clock, showing one of the infinitely possible times that the clock can represent. Compare that to a digital clock.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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An analog clock has the numbers in the hands, and it's analog because the motion of those hands is continuous. They can sweep across the circle, representing any of infinite times on that clock. For example, between 3.06 and 3.07, the minute hand is actually going to be at some point between those marks on the clock, showing one of the infinitely possible times that the clock can represent. Compare that to a digital clock. A digital clock is only going to show you 3.06 or 3.07. It will never display any of the many fractional seconds between those two times. Digital only takes on certain discrete values, and it has a finite number of those values.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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Compare that to a digital clock. A digital clock is only going to show you 3.06 or 3.07. It will never display any of the many fractional seconds between those two times. Digital only takes on certain discrete values, and it has a finite number of those values. So an analog wave or signal will smoothly sweep across the infinitely many possible values it has, while a digital wave or signal will only be at one of a number of discrete values, so the shape of the wave will be more square or step-like. Let's check out an example so this makes a little more sense. I like music, so we're going to talk about sound.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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Digital only takes on certain discrete values, and it has a finite number of those values. So an analog wave or signal will smoothly sweep across the infinitely many possible values it has, while a digital wave or signal will only be at one of a number of discrete values, so the shape of the wave will be more square or step-like. Let's check out an example so this makes a little more sense. I like music, so we're going to talk about sound. Sound is an analog signal or wave. So if we look at a graph of sound, volume over time, it's going to have a smooth, continuous analog waveform. Both the amplitude, or the volume, and the frequency, what we hear as pitch, are changing continuously between infinite possible values.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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I like music, so we're going to talk about sound. Sound is an analog signal or wave. So if we look at a graph of sound, volume over time, it's going to have a smooth, continuous analog waveform. Both the amplitude, or the volume, and the frequency, what we hear as pitch, are changing continuously between infinite possible values. And that's because sound waves, the vibration of particles propagating through the air, actually changes continuously. The very first sound recording and reproduction technology imprinted that analog wave directly onto a material. For example, records imprint that sound wave into vinyl, and cassettes imprint the sound wave onto tape.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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Both the amplitude, or the volume, and the frequency, what we hear as pitch, are changing continuously between infinite possible values. And that's because sound waves, the vibration of particles propagating through the air, actually changes continuously. The very first sound recording and reproduction technology imprinted that analog wave directly onto a material. For example, records imprint that sound wave into vinyl, and cassettes imprint the sound wave onto tape. A major drawback of this technology is that for the sound to play back exactly as it was recorded, that waveform needs to stay untouched, right? So think about scratching vinyl, or stretching or smudging a cassette tape. That's directly deforming the wave, so you'll never be able to reproduce the sound exactly as it was recorded.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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For example, records imprint that sound wave into vinyl, and cassettes imprint the sound wave onto tape. A major drawback of this technology is that for the sound to play back exactly as it was recorded, that waveform needs to stay untouched, right? So think about scratching vinyl, or stretching or smudging a cassette tape. That's directly deforming the wave, so you'll never be able to reproduce the sound exactly as it was recorded. So technology advanced, and sound waves became digitized. Here's how. Alright, so recall our analog sound wave.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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That's directly deforming the wave, so you'll never be able to reproduce the sound exactly as it was recorded. So technology advanced, and sound waves became digitized. Here's how. Alright, so recall our analog sound wave. We have a smooth analog wave that's taking on any number of infinitely possible values within this range. In order to digitize this wave, we're going to ascribe numbers to the amplitude at different points. Alright?
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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Alright, so recall our analog sound wave. We have a smooth analog wave that's taking on any number of infinitely possible values within this range. In order to digitize this wave, we're going to ascribe numbers to the amplitude at different points. Alright? Watch this magic. So we go over here and make a scale. So we're breaking up the amplitudes into discrete possibilities.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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Alright? Watch this magic. So we go over here and make a scale. So we're breaking up the amplitudes into discrete possibilities. Then we can go through the wave, and at specific points of the wave, measure what is the amplitude based on that scale. So over here, we're at the first point of the scale. At this peak, we're at the second point of our scale.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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So we're breaking up the amplitudes into discrete possibilities. Then we can go through the wave, and at specific points of the wave, measure what is the amplitude based on that scale. So over here, we're at the first point of the scale. At this peak, we're at the second point of our scale. Then the first, the third, the second, the fourth, back down to the first. Now that we have this wave broken up into discrete levels, right, we can ascribe the numbers and we effectively turn this analog wave into a set of numbers. One, two, one, three, two, four, one.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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At this peak, we're at the second point of our scale. Then the first, the third, the second, the fourth, back down to the first. Now that we have this wave broken up into discrete levels, right, we can ascribe the numbers and we effectively turn this analog wave into a set of numbers. One, two, one, three, two, four, one. Our wave has been digitized. Now that digitized wave can be played back through a speaker to recreate the analog wave. As long as the sampling happens at a quick enough rate, humans can't tell the difference.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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One, two, one, three, two, four, one. Our wave has been digitized. Now that digitized wave can be played back through a speaker to recreate the analog wave. As long as the sampling happens at a quick enough rate, humans can't tell the difference. Alright? So the digitization of waves is all about ascribing specific numbers to some of those mechanical properties of the wave. The important thing here is that now that the wave has been digitized, the digitized sound wave can be reliably stored, processed, and communicated with computers.
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Digital and analog information Information Technologies High School Physics Khan Academy.mp3
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As long as the sampling happens at a quick enough rate, humans can't tell the difference. Alright? So the digitization of waves is all about ascribing specific numbers to some of those mechanical properties of the wave. The important thing here is that now that the wave has been digitized, the digitized sound wave can be reliably stored, processed, and communicated with computers. So some information is lost in translation, but once the wave is digitized, its quality will never degrade. Okay? This allows for a lot more reliable technology because the wave is represented with numbers instead of it being physically imprinted on some material.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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Let me ask you a seemingly simple question. I have a picture of fire here, and my question is, what is fire? Well, what would you say if I were to tell you that fire, as we see it, these flickering flames, it is nothing but hot air? And I know what you might be thinking, hot air? Norm, I've seen air that's hot or I experienced air that's hot, and I don't oftentimes even see the air, but here I clearly see something bright, something that's emitting light, something that's emitting electromagnetic radiation. And then what I would say to you, if you were thinking that, is it actually turns out that anything in our universe that has a temperature above absolute zero, zero Kelvin, which is pretty much anything that you will ever come across in your life, emits electromagnetic radiation. Objects with temperature aren't the only way to create electromagnetic radiation, but it is a major way that's happening all around us.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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And I know what you might be thinking, hot air? Norm, I've seen air that's hot or I experienced air that's hot, and I don't oftentimes even see the air, but here I clearly see something bright, something that's emitting light, something that's emitting electromagnetic radiation. And then what I would say to you, if you were thinking that, is it actually turns out that anything in our universe that has a temperature above absolute zero, zero Kelvin, which is pretty much anything that you will ever come across in your life, emits electromagnetic radiation. Objects with temperature aren't the only way to create electromagnetic radiation, but it is a major way that's happening all around us. Even if you were in a pitch black room, you would be emitting electromagnetic radiation. A tree outside, even if it was dark outside, is emitting electromagnetic radiation. You might say, wait, but I don't see the tree, and that's because your eyes can only detect certain frequencies of electromagnetic radiation.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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Objects with temperature aren't the only way to create electromagnetic radiation, but it is a major way that's happening all around us. Even if you were in a pitch black room, you would be emitting electromagnetic radiation. A tree outside, even if it was dark outside, is emitting electromagnetic radiation. You might say, wait, but I don't see the tree, and that's because your eyes can only detect certain frequencies of electromagnetic radiation. If we look at this diagram right over here, we can see how we've categorized many of the frequencies, and you can see that up here, this is the frequency, this is the wavelength, and these are in powers of 10. So you can really view this as a logarithmic scale. And just over here, you can see that our eyes can only visibly see a small section of this logarithmic scale of frequencies.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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You might say, wait, but I don't see the tree, and that's because your eyes can only detect certain frequencies of electromagnetic radiation. If we look at this diagram right over here, we can see how we've categorized many of the frequencies, and you can see that up here, this is the frequency, this is the wavelength, and these are in powers of 10. So you can really view this as a logarithmic scale. And just over here, you can see that our eyes can only visibly see a small section of this logarithmic scale of frequencies. One of the things I like to wonder is if humans didn't have eyes, if we weren't able to detect even the small segment of the electromagnetic spectrum, would we even know that something like electromagnetic waves existed? But we could see you have gamma rays, X-rays, UV rays, infrared rays, microwave, FM, AM radio waves, long radio waves, and most hot air, the frequency isn't high enough for us to see it. So most hot air is going to be in the infrared range.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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And just over here, you can see that our eyes can only visibly see a small section of this logarithmic scale of frequencies. One of the things I like to wonder is if humans didn't have eyes, if we weren't able to detect even the small segment of the electromagnetic spectrum, would we even know that something like electromagnetic waves existed? But we could see you have gamma rays, X-rays, UV rays, infrared rays, microwave, FM, AM radio waves, long radio waves, and most hot air, the frequency isn't high enough for us to see it. So most hot air is going to be in the infrared range. Only if it gets hot enough will we start to see it, and that's what's happening with this fire here. And if you look closely at a fire, you might actually see that the location where the combustion reaction is happening, that that actually might be dark. And then right above that, you'll see some blue flame.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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So most hot air is going to be in the infrared range. Only if it gets hot enough will we start to see it, and that's what's happening with this fire here. And if you look closely at a fire, you might actually see that the location where the combustion reaction is happening, that that actually might be dark. And then right above that, you'll see some blue flame. And then you'll see, maybe if you look closely, some green or yellow flame, and then you will see the orange flame, and then you will see the red flame. And the reason why it might be dark right where the combustion reaction is happening is that might be very high-energy electromagnetic waves. That would be in the UV spectrum.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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And then right above that, you'll see some blue flame. And then you'll see, maybe if you look closely, some green or yellow flame, and then you will see the orange flame, and then you will see the red flame. And the reason why it might be dark right where the combustion reaction is happening is that might be very high-energy electromagnetic waves. That would be in the UV spectrum. That would be at a higher frequency than what's visible, so to our eyes, it looks dark. And then as it cools, it goes through the visible spectrum, and then if it cools enough, it goes to infrared. But we human beings have built the capability to see beyond what our regular eyes can see.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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That would be in the UV spectrum. That would be at a higher frequency than what's visible, so to our eyes, it looks dark. And then as it cools, it goes through the visible spectrum, and then if it cools enough, it goes to infrared. But we human beings have built the capability to see beyond what our regular eyes can see. For example, these are what are often known as thermal images, but they're really just detecting the infrared range. So this is a picture of two dogs. It could be pitch black outside.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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But we human beings have built the capability to see beyond what our regular eyes can see. For example, these are what are often known as thermal images, but they're really just detecting the infrared range. So this is a picture of two dogs. It could be pitch black outside. I mean, it could be the middle of the night, but because they have temperature, they are releasing electromagnetic waves, which we can detect. And this over here has a scale of what the temperature must be. So you can see the eyes of the dog are the hottest part right over here.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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It could be pitch black outside. I mean, it could be the middle of the night, but because they have temperature, they are releasing electromagnetic waves, which we can detect. And this over here has a scale of what the temperature must be. So you can see the eyes of the dog are the hottest part right over here. You can also see thermal imaging of not only a hand, but after a hand has touched a wall. With our eyes, if you were to touch a wall for say 30 seconds, it doesn't look like the wall has changed at all. But if you were to look at the infrared, you would see that you would have heated up parts of the wall, and you would be able to see the shape of a hand.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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So you can see the eyes of the dog are the hottest part right over here. You can also see thermal imaging of not only a hand, but after a hand has touched a wall. With our eyes, if you were to touch a wall for say 30 seconds, it doesn't look like the wall has changed at all. But if you were to look at the infrared, you would see that you would have heated up parts of the wall, and you would be able to see the shape of a hand. And so you could imagine, we human beings, because of our ability to detect electromagnetic waves and explore electromagnetic waves, we've been able to leverage them more and more in our everyday lives. Thermal imaging itself has a lot of applications. Firefighters use it to find people or to find flames in the middle of a lot of smoke.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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But if you were to look at the infrared, you would see that you would have heated up parts of the wall, and you would be able to see the shape of a hand. And so you could imagine, we human beings, because of our ability to detect electromagnetic waves and explore electromagnetic waves, we've been able to leverage them more and more in our everyday lives. Thermal imaging itself has a lot of applications. Firefighters use it to find people or to find flames in the middle of a lot of smoke. We have things like X-rays, which are high energy electromagnetic waves, which we can use to see through soft tissues. So we can see bones. This is an old image, and it looks like they're using the X-rays kind of carelessly.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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Firefighters use it to find people or to find flames in the middle of a lot of smoke. We have things like X-rays, which are high energy electromagnetic waves, which we can use to see through soft tissues. So we can see bones. This is an old image, and it looks like they're using the X-rays kind of carelessly. You don't wanna be throwing that radiation around. But even today, I got an X-ray of my teeth just the other day when I went to the dentist. When you talk on your cell phone, the way that your cell phone is able to communicate is leveraging electromagnetic waves.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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This is an old image, and it looks like they're using the X-rays kind of carelessly. You don't wanna be throwing that radiation around. But even today, I got an X-ray of my teeth just the other day when I went to the dentist. When you talk on your cell phone, the way that your cell phone is able to communicate is leveraging electromagnetic waves. This is another thing that's mind-blowing to me is that my little cell phone can actually emit electromagnetic waves in the radio part of the spectrum far enough to be received by a cell tower that could be 10, 20, and in certain cases, 30 or 40 miles away. Microwave ovens literally release microwaves, which are absorbed by our food, which heats up the food. And so I'll leave you there.
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Electromagnetic radiation emission Electromagnetic Radiation High School Physics Khan Academy.mp3
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When you talk on your cell phone, the way that your cell phone is able to communicate is leveraging electromagnetic waves. This is another thing that's mind-blowing to me is that my little cell phone can actually emit electromagnetic waves in the radio part of the spectrum far enough to be received by a cell tower that could be 10, 20, and in certain cases, 30 or 40 miles away. Microwave ovens literally release microwaves, which are absorbed by our food, which heats up the food. And so I'll leave you there. The big picture here is that electromagnetic waves are all around us. It's most obvious to us in the visible spectrum because that's what we can see, but there's a large continuum of different frequencies that the visible is only a part of. And we human beings have leveraged this phenomenon in all sorts of interesting ways.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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In previous videos, we have already defined or provided a definition for energy as the capacity to do work. We have also talked about the notion of a field. We have talked about things like an electric field or a gravitational field. And these are really mental constructs that we have produced to explain force at a distance. For example, if I have a planet here and then I have some other object here that has some mass, we know that these are going to exert forces on each other and actually equal and opposite forces on each other. And scientists said, well, they're not touching each other. How are they exerting forces on each other?
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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And these are really mental constructs that we have produced to explain force at a distance. For example, if I have a planet here and then I have some other object here that has some mass, we know that these are going to exert forces on each other and actually equal and opposite forces on each other. And scientists said, well, they're not touching each other. How are they exerting forces on each other? And so they introduced this notion of a field that each of these objects produce a gravitational field of sorts. Now, Einstein came later and said, well, actually they're warping space-time, et cetera, but a field is one way to think about how they're able to induce a force, so to speak, in each other. Similarly, if you have two electric charges, let's say you have two negative point charges like that, we know that they push away on each other, that like charges repel.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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How are they exerting forces on each other? And so they introduced this notion of a field that each of these objects produce a gravitational field of sorts. Now, Einstein came later and said, well, actually they're warping space-time, et cetera, but a field is one way to think about how they're able to induce a force, so to speak, in each other. Similarly, if you have two electric charges, let's say you have two negative point charges like that, we know that they push away on each other, that like charges repel. Well, they're not touching each other. How do they know to have a force being applied to them in opposite directions? So once again, there's this idea that each of these produces a field, the other one is in the other electric charges field, and then that field somehow applies that force or makes that force happen to the other thing.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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Similarly, if you have two electric charges, let's say you have two negative point charges like that, we know that they push away on each other, that like charges repel. Well, they're not touching each other. How do they know to have a force being applied to them in opposite directions? So once again, there's this idea that each of these produces a field, the other one is in the other electric charges field, and then that field somehow applies that force or makes that force happen to the other thing. Notice, the field is a useful concept to predict what will happen and to quantify how it could happen, but it really is just something in our minds to make sense of the universe. So with that out of the way, let's look at this water wheel right over here. You can see that the water comes down from here and then it falls, and as it falls, it pushes, it fills up these things right over here, which then pushes them down, and then the whole wheel turns.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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So once again, there's this idea that each of these produces a field, the other one is in the other electric charges field, and then that field somehow applies that force or makes that force happen to the other thing. Notice, the field is a useful concept to predict what will happen and to quantify how it could happen, but it really is just something in our minds to make sense of the universe. So with that out of the way, let's look at this water wheel right over here. You can see that the water comes down from here and then it falls, and as it falls, it pushes, it fills up these things right over here, which then pushes them down, and then the whole wheel turns. And then that wheel could do work, actually could do useful work. In a physics context, not all work is necessarily useful, but this could actually do useful work. So what I wanna think about is two different drops of water.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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You can see that the water comes down from here and then it falls, and as it falls, it pushes, it fills up these things right over here, which then pushes them down, and then the whole wheel turns. And then that wheel could do work, actually could do useful work. In a physics context, not all work is necessarily useful, but this could actually do useful work. So what I wanna think about is two different drops of water. I have a drop of water here, maybe the same drop of water. When it's up here versus once it has gone all the way down and has been dumped into what I'm assuming is a stream down here. Now, which one has a higher capacity to do work?
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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So what I wanna think about is two different drops of water. I have a drop of water here, maybe the same drop of water. When it's up here versus once it has gone all the way down and has been dumped into what I'm assuming is a stream down here. Now, which one has a higher capacity to do work? Pause this video and think about that. Well, I just told you that when the water drop is up here, it has the capacity as it falls because of the gravitational field, which is pulling down on it. And by the way, if the gravitational field is pulling down on the water drop, that water drop is also pulling up on earth.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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Now, which one has a higher capacity to do work? Pause this video and think about that. Well, I just told you that when the water drop is up here, it has the capacity as it falls because of the gravitational field, which is pulling down on it. And by the way, if the gravitational field is pulling down on the water drop, that water drop is also pulling up on earth. But this gravitational field of earth is pulling down on that water drop. And because of that, if the water drop is not supported, it can actually do work in this example on its way to being in this position right over here. Now, this position right over here, in theory, it could maybe still do work.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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And by the way, if the gravitational field is pulling down on the water drop, that water drop is also pulling up on earth. But this gravitational field of earth is pulling down on that water drop. And because of that, if the water drop is not supported, it can actually do work in this example on its way to being in this position right over here. Now, this position right over here, in theory, it could maybe still do work. Maybe there's a cliff right over here and it can continue to pour down. But the water drop up here clearly has the capacity to do more work because it has the potential work that it can do from going from here to here. And then obviously it could then continue to do any work that this position would allow it to have.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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Now, this position right over here, in theory, it could maybe still do work. Maybe there's a cliff right over here and it can continue to pour down. But the water drop up here clearly has the capacity to do more work because it has the potential work that it can do from going from here to here. And then obviously it could then continue to do any work that this position would allow it to have. So we would say that this water drop, by virtue of its position, has a higher capacity to do work and has more energy. And what is the form of that energy? Well, in this case, it's gravitational potential energy.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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And then obviously it could then continue to do any work that this position would allow it to have. So we would say that this water drop, by virtue of its position, has a higher capacity to do work and has more energy. And what is the form of that energy? Well, in this case, it's gravitational potential energy. It's energy that is stored, and I put that in quotes because it's not like you're going to be able to open that water drop and all of a sudden see energy, but it's energy that's stored by virtue of its position. Another way to think about it is, instead of imagining that the energy is stored in the water drop, and it is really happening in our minds, is to say that that energy is stored in the field, in this case, this gravitational field. Now, the gravitational field is pulling on this water drop, so the direction of motion would actually reduce the energy in the field.
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Energy and fields Introduction to energy High school physics Khan Academy.mp3
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Well, in this case, it's gravitational potential energy. It's energy that is stored, and I put that in quotes because it's not like you're going to be able to open that water drop and all of a sudden see energy, but it's energy that's stored by virtue of its position. Another way to think about it is, instead of imagining that the energy is stored in the water drop, and it is really happening in our minds, is to say that that energy is stored in the field, in this case, this gravitational field. Now, the gravitational field is pulling on this water drop, so the direction of motion would actually reduce the energy in the field. So if we just let things happen, Earth's gravitational field is going to pull on this water drop, and actually that water drop has a gravitational field that's going to pull up on Earth, but as that water drop gets pulled down, the total amount of energy stored in the field is going to go down. Now, what happened to that energy? That energy gets transferred out of the field into kinetic energy of this wheel, which could then be transferred into other things.
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Effects of different wavelengths of radiation Electromagnetic Radiation Khan Academy.mp3
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We know that the longer the wavelength, the lower the frequency, and the shorter the wavelength, the higher the frequency. Now, what's also interesting about electromagnetic waves is that everything in the universe that has any temperature at all, which is most things in the universe, will emit electromagnetic waves. You might look at yourself right now and say, wait, am I emitting electromagnetic waves? Well, you're probably not emitting visible waves. You're reflecting visible waves. That's why you can see your hand. But your body is emitting infrared waves.
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Effects of different wavelengths of radiation Electromagnetic Radiation Khan Academy.mp3
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Well, you're probably not emitting visible waves. You're reflecting visible waves. That's why you can see your hand. But your body is emitting infrared waves. Now, just as almost everything can emit waves, waves can also be absorbed depending on the material, depending on the size of the object. Now, generally speaking, when electromagnetic waves are absorbed by some substance, it's turned into thermal energy. You can experience that.
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Effects of different wavelengths of radiation Electromagnetic Radiation Khan Academy.mp3
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But your body is emitting infrared waves. Now, just as almost everything can emit waves, waves can also be absorbed depending on the material, depending on the size of the object. Now, generally speaking, when electromagnetic waves are absorbed by some substance, it's turned into thermal energy. You can experience that. Go outside on a sunny day, wear a black shirt, and a black shirt is not reflecting much visible light, and so it's all being absorbed, or most of it is being absorbed, and it gets converted to heat. You will get much hotter than a friend who is wearing a white T-shirt. Now, we have to be pretty careful as we get to higher frequencies than visible light.
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Effects of different wavelengths of radiation Electromagnetic Radiation Khan Academy.mp3
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You can experience that. Go outside on a sunny day, wear a black shirt, and a black shirt is not reflecting much visible light, and so it's all being absorbed, or most of it is being absorbed, and it gets converted to heat. You will get much hotter than a friend who is wearing a white T-shirt. Now, we have to be pretty careful as we get to higher frequencies than visible light. Ultraviolet light, that's what's causing sunburn, and the risks only increase as you get to higher frequencies like X-rays and gamma rays. What these really high-frequency electromagnetic waves can do is knock out electrons from atoms, which would ionize them, which would change their chemical properties. That could affect DNA.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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But here's a question. If someone else on the other end of this string also sent a wave pulse down the line toward the first wave, what would happen when they overlap? So let's try to figure this out. Let's say you had a wave coming in this way, and yes, this is square. Kind of weird. It'd be hard. You have to be pretty talented to do this on a string, but this doesn't have to be a string.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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Let's say you had a wave coming in this way, and yes, this is square. Kind of weird. It'd be hard. You have to be pretty talented to do this on a string, but this doesn't have to be a string. Let's say it could be a sound wave, an electromagnetic wave, any wave at all. The fact that it's a square is just gonna make it easier for us to analyze. So you got this wave coming in this way, and then another wave coming in this way.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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You have to be pretty talented to do this on a string, but this doesn't have to be a string. Let's say it could be a sound wave, an electromagnetic wave, any wave at all. The fact that it's a square is just gonna make it easier for us to analyze. So you got this wave coming in this way, and then another wave coming in this way. So to be clear, this is the same string. There aren't like two strings here. There is one string, two waves coming at each other.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So you got this wave coming in this way, and then another wave coming in this way. So to be clear, this is the same string. There aren't like two strings here. There is one string, two waves coming at each other. So to be real, I mean, honestly, there's only one string. So this should be string coming here, and then there's a pulse up this way. So this string shouldn't be here.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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There is one string, two waves coming at each other. So to be real, I mean, honestly, there's only one string. So this should be string coming here, and then there's a pulse up this way. So this string shouldn't be here. This string moved up to that point, it got disturbed, then it comes back down to zero. And then there shouldn't be two strings here. You don't have two strings in the same spot.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So this string shouldn't be here. This string moved up to that point, it got disturbed, then it comes back down to zero. And then there shouldn't be two strings here. You don't have two strings in the same spot. So this would be the string up there, and then it comes back down. But in these examples, I don't wanna have to erase these all the time. It'd make the video really long.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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You don't have two strings in the same spot. So this would be the string up there, and then it comes back down. But in these examples, I don't wanna have to erase these all the time. It'd make the video really long. So let's just, anytime there's a string underneath a pulse, we're just gonna pretend like there's no string in there. So what would happen? What would happen when these pulses overlap?
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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It'd make the video really long. So let's just, anytime there's a string underneath a pulse, we're just gonna pretend like there's no string in there. So what would happen? What would happen when these pulses overlap? Well, let's just find out. If I take one, and I move this here, and then another wave is gonna move over the top of that one, I'm gonna get wave interference. This is the term, wave interference, for when two or more waves overlap in the same region.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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What would happen when these pulses overlap? Well, let's just find out. If I take one, and I move this here, and then another wave is gonna move over the top of that one, I'm gonna get wave interference. This is the term, wave interference, for when two or more waves overlap in the same region. So what's gonna happen? Well, the string can't be in two places at once. There can only be one string and one shape of that string.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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This is the term, wave interference, for when two or more waves overlap in the same region. So what's gonna happen? Well, the string can't be in two places at once. There can only be one string and one shape of that string. And the way you find out what the total wave is gonna look like is simply by adding up the contributions of the two waves that are overlapping. So in other words, if I wanna know the height of the total wave, I'm gonna call that height yt, t for total. That's just gonna equal the height of the first wave, I'll call that y1, plus the height of the second wave, and I'll call that y2.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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There can only be one string and one shape of that string. And the way you find out what the total wave is gonna look like is simply by adding up the contributions of the two waves that are overlapping. So in other words, if I wanna know the height of the total wave, I'm gonna call that height yt, t for total. That's just gonna equal the height of the first wave, I'll call that y1, plus the height of the second wave, and I'll call that y2. So if you're familiar with the wave equations, you can just plug in those two wave equations here, add them up, and you get a total wave equation. But a lot of times, you don't have to resort to the full-blown mathematics of the wave equation. You can kinda just look at the picture and figure out what the total wave would look like.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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That's just gonna equal the height of the first wave, I'll call that y1, plus the height of the second wave, and I'll call that y2. So if you're familiar with the wave equations, you can just plug in those two wave equations here, add them up, and you get a total wave equation. But a lot of times, you don't have to resort to the full-blown mathematics of the wave equation. You can kinda just look at the picture and figure out what the total wave would look like. So let's do that. Let's put a little backdrop here so we can add these up. So we'll call this one unit high, and there's gonna be two units high, and there's gonna be three units high.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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You can kinda just look at the picture and figure out what the total wave would look like. So let's do that. Let's put a little backdrop here so we can add these up. So we'll call this one unit high, and there's gonna be two units high, and there's gonna be three units high. It could be meters or centimeters, but it doesn't matter. We'll just say one unit, two unit, three unit. And now to figure out what the total wave's gonna look like, I just add up the contributions from each individual wave.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So we'll call this one unit high, and there's gonna be two units high, and there's gonna be three units high. It could be meters or centimeters, but it doesn't matter. We'll just say one unit, two unit, three unit. And now to figure out what the total wave's gonna look like, I just add up the contributions from each individual wave. So both waves are zero over here, so that's easy. Zero plus zero is zero. And then it gets to here.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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And now to figure out what the total wave's gonna look like, I just add up the contributions from each individual wave. So both waves are zero over here, so that's easy. Zero plus zero is zero. And then it gets to here. The blue wave, we'll call that wave one, has a value of one unit high. The pink wave, we'll call that wave two, has a value of two units high. They're going in different directions, doesn't matter.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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And then it gets to here. The blue wave, we'll call that wave one, has a value of one unit high. The pink wave, we'll call that wave two, has a value of two units high. They're going in different directions, doesn't matter. Right now, they're overlapping. So one unit high plus two units high is gonna be equal to three units high. My total wave would look something like this.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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They're going in different directions, doesn't matter. Right now, they're overlapping. So one unit high plus two units high is gonna be equal to three units high. My total wave would look something like this. So if I were to ask what would the wave actually look like, the string, if this were a string, would actually look like this. It would just be one big three unit high wave, all those two waves are overlapping. So that one was kinda easy.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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My total wave would look something like this. So if I were to ask what would the wave actually look like, the string, if this were a string, would actually look like this. It would just be one big three unit high wave, all those two waves are overlapping. So that one was kinda easy. How does this get harder? Well, let's say we ask the question, what do these two waves look like when they're only partially overlapping? So maybe when they get to this point, where they're only halfway overlapped, what's that total wave gonna look like?
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So that one was kinda easy. How does this get harder? Well, let's say we ask the question, what do these two waves look like when they're only partially overlapping? So maybe when they get to this point, where they're only halfway overlapped, what's that total wave gonna look like? We're still gonna use this rule. We're gonna add up both contributions to get the total. So over here, we have zero, and zero plus zero is zero.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So maybe when they get to this point, where they're only halfway overlapped, what's that total wave gonna look like? We're still gonna use this rule. We're gonna add up both contributions to get the total. So over here, we have zero, and zero plus zero is zero. Until you get to here. Now the blue wave, wave one, has a value of one unit high. The height of this wave is one unit.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So over here, we have zero, and zero plus zero is zero. Until you get to here. Now the blue wave, wave one, has a value of one unit high. The height of this wave is one unit. The height of the pink wave, wave two, is zero units. One plus zero is one. So my total wave would look like this in that region.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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The height of this wave is one unit. The height of the pink wave, wave two, is zero units. One plus zero is one. So my total wave would look like this in that region. And now in this region, the blue wave is one unit high. The pink wave is two units high. One plus two is three.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So my total wave would look like this in that region. And now in this region, the blue wave is one unit high. The pink wave is two units high. One plus two is three. So it would look like this in this region. Now over here, since the blue wave dropped down, we have to figure out a new value. So the blue wave has a value of zero.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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One plus two is three. So it would look like this in this region. Now over here, since the blue wave dropped down, we have to figure out a new value. So the blue wave has a value of zero. The pink wave has a value of two. Two plus zero is two. And so my total wave's gonna look like this.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So the blue wave has a value of zero. The pink wave has a value of two. Two plus zero is two. And so my total wave's gonna look like this. So the total string, when those are overlapping halfway, would look something like this. Which, if it was a string, would be really hard to do, because it's hard to get an exactly square wave. But electronic signals can have square waves, and this is what they would look like if they were overlapping.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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And so my total wave's gonna look like this. So the total string, when those are overlapping halfway, would look something like this. Which, if it was a string, would be really hard to do, because it's hard to get an exactly square wave. But electronic signals can have square waves, and this is what they would look like if they were overlapping. Now I wanna warn you about one thing. This idea of wave interference is a cool idea, but you gotta be careful. The term interference is a little misleading.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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But electronic signals can have square waves, and this is what they would look like if they were overlapping. Now I wanna warn you about one thing. This idea of wave interference is a cool idea, but you gotta be careful. The term interference is a little misleading. Yes, while these waves are overlapping, they create a different wave. They get distorted because the total wave will be the sum of the two waves. But these waves pass right through each other, which is great, because when our phones send out a text message or a call to someone else, everyone else's phone is also sending out a message in that same air.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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The term interference is a little misleading. Yes, while these waves are overlapping, they create a different wave. They get distorted because the total wave will be the sum of the two waves. But these waves pass right through each other, which is great, because when our phones send out a text message or a call to someone else, everyone else's phone is also sending out a message in that same air. Those electromagnetic waves are traveling right through each other. If they bounced off of each other, if these waves like bounced or got corrupted and the information got changed so that the shape isn't the same after as it was before, it'd be really hard to make phone calls and send text messages. But the wave interference is only happening while they're overlapping.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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But these waves pass right through each other, which is great, because when our phones send out a text message or a call to someone else, everyone else's phone is also sending out a message in that same air. Those electromagnetic waves are traveling right through each other. If they bounced off of each other, if these waves like bounced or got corrupted and the information got changed so that the shape isn't the same after as it was before, it'd be really hard to make phone calls and send text messages. But the wave interference is only happening while they're overlapping. The waves make it through unaffected. So the interference is only happening while they're overlapping. Otherwise, they pass right through each other unaffected, which is good.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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But the wave interference is only happening while they're overlapping. The waves make it through unaffected. So the interference is only happening while they're overlapping. Otherwise, they pass right through each other unaffected, which is good. So let's look at one more example that's a little more challenging. So I'm gonna get rid of these. And let's say you had these two wave pulses, the same square pulse, but then you got this weird triangular pulse coming in and they're gonna overlap.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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Otherwise, they pass right through each other unaffected, which is good. So let's look at one more example that's a little more challenging. So I'm gonna get rid of these. And let's say you had these two wave pulses, the same square pulse, but then you got this weird triangular pulse coming in and they're gonna overlap. So this wave pulse makes it to here. This triangular pulse makes it to here. Oh, and you get the state of Nevada.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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And let's say you had these two wave pulses, the same square pulse, but then you got this weird triangular pulse coming in and they're gonna overlap. So this wave pulse makes it to here. This triangular pulse makes it to here. Oh, and you get the state of Nevada. So the string is not gonna take the shape of Nevada. The string can't be in two places at once. So what's our total wave gonna look like?
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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Oh, and you get the state of Nevada. So the string is not gonna take the shape of Nevada. The string can't be in two places at once. So what's our total wave gonna look like? We're gonna use the same rules that we did before for wave interference. We're gonna add up the values of each wave at a particular point to get the value of the total wave at that point. So what do we get?
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So what's our total wave gonna look like? We're gonna use the same rules that we did before for wave interference. We're gonna add up the values of each wave at a particular point to get the value of the total wave at that point. So what do we get? We've got zero plus zero over here, so that's easy. And now at this moment, the value of the blue wave is one. The value of the pink wave is zero.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So what do we get? We've got zero plus zero over here, so that's easy. And now at this moment, the value of the blue wave is one. The value of the pink wave is zero. So zero plus one is one. And in here, it's a little weird. Like you've got this pink wave changing, but over here it's easy because the blue wave has a value of one.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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The value of the pink wave is zero. So zero plus one is one. And in here, it's a little weird. Like you've got this pink wave changing, but over here it's easy because the blue wave has a value of one. The pink wave, let's assume this drops down one as well. So this is a negative one unit. Blue wave is one, pink wave is negative one.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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Like you've got this pink wave changing, but over here it's easy because the blue wave has a value of one. The pink wave, let's assume this drops down one as well. So this is a negative one unit. Blue wave is one, pink wave is negative one. That's gonna be zero. One plus negative one is zero. And after there, it's gonna be zero.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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Blue wave is one, pink wave is negative one. That's gonna be zero. One plus negative one is zero. And after there, it's gonna be zero. But what is it in between? Well, the simplest answer is actually the correct answer here. It just drops down like this.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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And after there, it's gonna be zero. But what is it in between? Well, the simplest answer is actually the correct answer here. It just drops down like this. Why does it do that? Well, let's consider a point in the middle. This point in the middle, the blue wave has a value of one.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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It just drops down like this. Why does it do that? Well, let's consider a point in the middle. This point in the middle, the blue wave has a value of one. The pink wave has a value of negative a half. So one plus negative a half is positive one half. Or consider a point over here, the value of the wave right here.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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This point in the middle, the blue wave has a value of one. The pink wave has a value of negative a half. So one plus negative a half is positive one half. Or consider a point over here, the value of the wave right here. For the blue wave is one. The value of the pink wave is like negative three fourths. So the value of the total wave would be positive one fourth.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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Or consider a point over here, the value of the wave right here. For the blue wave is one. The value of the pink wave is like negative three fourths. So the value of the total wave would be positive one fourth. That's why this drops down linearly. If this is linear, this pink wave just keeps taking a bigger and bigger bite out of this blue wave. And the total wave would look like this.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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So the value of the total wave would be positive one fourth. That's why this drops down linearly. If this is linear, this pink wave just keeps taking a bigger and bigger bite out of this blue wave. And the total wave would look like this. So if we get rid of these, this would be what the total wave looks like when these two waves overlap. So I should say that this technique of just adding up the values of each wave at that point, it's called the superposition principle. It's a very lofty, intimidating name for something that's actually pretty simple.
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Wave interference Mechanical waves and sound Physics Khan Academy.mp3
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And the total wave would look like this. So if we get rid of these, this would be what the total wave looks like when these two waves overlap. So I should say that this technique of just adding up the values of each wave at that point, it's called the superposition principle. It's a very lofty, intimidating name for something that's actually pretty simple. To find the total wave, you just add up the values of the individual waves. So recapping, wave interference is the term we use to refer to the situation where two or more waves are overlapping in the same region. And to find the value of the total wave while they're overlapping, you can use the superposition principle, which just says to add up the values of the individual waves at a given point to find the value of the total wave at that point.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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And when we talk about energy, we're talking about its capacity to do work. So just based on that early definition of kinetic energy, which of these two running backs do you think has more kinetic energy? This gentleman on the left whose mass is 100 kilograms and who is traveling at a speed of two meters per second, or the gentleman on the right who has a mass of 25 kilograms and who's traveling with a speed of four meters per second. Pause this video and think about that. All right, now let's think about this together. So I'm first just going to give you the formula for kinetic energy, but then we are going to derive it. So the formula for kinetic energy is that it's equal to 1 1⁄2 times the mass of the object times the magnitude of its velocity squared, or another way to think about it, it's speed squared.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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Pause this video and think about that. All right, now let's think about this together. So I'm first just going to give you the formula for kinetic energy, but then we are going to derive it. So the formula for kinetic energy is that it's equal to 1 1⁄2 times the mass of the object times the magnitude of its velocity squared, or another way to think about it, it's speed squared. And so given this formula, pause the video and see if you can calculate the kinetic energy for each of these running backs. All right, let's calculate the kinetic energy for this guy on the left. It's going to be 1 1⁄2 times his mass, which is 100 kilograms, times the square of the speed.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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So the formula for kinetic energy is that it's equal to 1 1⁄2 times the mass of the object times the magnitude of its velocity squared, or another way to think about it, it's speed squared. And so given this formula, pause the video and see if you can calculate the kinetic energy for each of these running backs. All right, let's calculate the kinetic energy for this guy on the left. It's going to be 1 1⁄2 times his mass, which is 100 kilograms, times the square of the speed. So times four meters squared per second squared. Have to make sure that we square the units as well. And this is going to be equal to 1 1⁄2 times 100 is 50 times four is 200.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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It's going to be 1 1⁄2 times his mass, which is 100 kilograms, times the square of the speed. So times four meters squared per second squared. Have to make sure that we square the units as well. And this is going to be equal to 1 1⁄2 times 100 is 50 times four is 200. And then the units are kilogram meter squared per second squared. And you might already recognize that this is the same thing as kilogram meter per second squared times meters, or these are really the units of force times distance, or this is the units of energy, which we can write as 200 joules. Now let's do the same thing for this running back that has less mass.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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And this is going to be equal to 1 1⁄2 times 100 is 50 times four is 200. And then the units are kilogram meter squared per second squared. And you might already recognize that this is the same thing as kilogram meter per second squared times meters, or these are really the units of force times distance, or this is the units of energy, which we can write as 200 joules. Now let's do the same thing for this running back that has less mass. Kinetic energy here is going to be 1 1⁄2 times the mass, 25 kilograms, times the square of the speed here. So that's going to be 16 meters squared per second squared. And then that gets us, we're essentially gonna have 1 1⁄2 times 16 is eight times 25, 200.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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Now let's do the same thing for this running back that has less mass. Kinetic energy here is going to be 1 1⁄2 times the mass, 25 kilograms, times the square of the speed here. So that's going to be 16 meters squared per second squared. And then that gets us, we're essentially gonna have 1 1⁄2 times 16 is eight times 25, 200. And we get the exact same units, and so we can go straight to 200 joules. So it turns out that they have the exact same kinetic energy. Even though the gentleman on the right has 1⁄4 the mass and only twice the speed, we see that we square the speed right over here.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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And then that gets us, we're essentially gonna have 1 1⁄2 times 16 is eight times 25, 200. And we get the exact same units, and so we can go straight to 200 joules. So it turns out that they have the exact same kinetic energy. Even though the gentleman on the right has 1⁄4 the mass and only twice the speed, we see that we square the speed right over here. So that makes a huge difference. And so their energy due to their motion, they have the same capacity to do work. Now, some of you are thinking, where does this formula come from?
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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Even though the gentleman on the right has 1⁄4 the mass and only twice the speed, we see that we square the speed right over here. So that makes a huge difference. And so their energy due to their motion, they have the same capacity to do work. Now, some of you are thinking, where does this formula come from? And one way to think about work and energy is that you can use work to transfer energy to a system or to an object somehow. And then that energy is that object's capacity to do work again. So let's imagine some object that has a mass m and the magnitude of its velocity or its speed is v. So what would be the work necessary to bring that object that has mass m to a speed of v, assuming it's starting at a standstill?
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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Now, some of you are thinking, where does this formula come from? And one way to think about work and energy is that you can use work to transfer energy to a system or to an object somehow. And then that energy is that object's capacity to do work again. So let's imagine some object that has a mass m and the magnitude of its velocity or its speed is v. So what would be the work necessary to bring that object that has mass m to a speed of v, assuming it's starting at a standstill? Well, let's think about it a little bit. Work is equal to the magnitude of force in a certain direction times the magnitude of the displacement in that direction, which we could write like that. Sometimes they use s for the magnitude of displacement as well.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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So let's imagine some object that has a mass m and the magnitude of its velocity or its speed is v. So what would be the work necessary to bring that object that has mass m to a speed of v, assuming it's starting at a standstill? Well, let's think about it a little bit. Work is equal to the magnitude of force in a certain direction times the magnitude of the displacement in that direction, which we could write like that. Sometimes they use s for the magnitude of displacement as well. And so what is the force the same thing as? We know that the force is the same thing as mass times the acceleration. And we're going to assume that we have constant acceleration just so that we can simplify our derivation here.
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Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3
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Sometimes they use s for the magnitude of displacement as well. And so what is the force the same thing as? We know that the force is the same thing as mass times the acceleration. And we're going to assume that we have constant acceleration just so that we can simplify our derivation here. And then what's the distance we're going to travel? Well, the distance is going to be the average magnitude of the velocity, or we could say the average speed, so I'll write it like this, times the time that it takes to accelerate the object to a velocity of v. Well, how long does it take to accelerate an object to a velocity of v if you're accelerating it at a? Well, this is just going to be the velocity divided by the acceleration.
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