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Anderson Video - Motion Diagram of Accelerating Car

Professor Anderson
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 >> Hello class, Professor Anderson here. Let's talk a little bit about motion diagrams. And this is a way to sort of visualize the movements of objects in the universe. And let's just think about a person running for a second. If I took a stroboscopic picture of a person running, what would it look like? Well, the first flash would go off, and they would be in that position there. And now, awhile later, I take another position, take another flash, and so on. Okay? And pretend that their legs are actually moving in between those shots. Okay. And now we go to the next one, and now we go to the next one, and so forth. Person is moving to the right. Like so. This is what a motion diagram looks like. It's just a snapshot of this person. And in the old days, when we used to have film cameras-you guys ever heard of this thing called film? We used to be able to open the shutter, expose the film for a very long time, and just take strobe pictures as somebody went by. And you would get five different shots of them as they moved. Now, looking at this, you already have a lot of information. Is their position increasing or decreasing? >> (student speaking) Increasing. >> Okay. Somebody said increasing, but they hesitated. Why did they hesitate? Because we didn't decide which direction was positive or negative. So you have to do that first. Let's say that this is positive to the right. And they start at x equals zero. Okay? Their position is increasing. Now, just based on this picture, you already know a lot more information. Are they increasing their speed? Decreasing their speed? Or staying the same. All right. She identified there is something very important here, which is the delta between these pictures. There is a different delta there than there. Now I could get out the measuring tape and see. I was trying to draw them a little closer together, but I can certainly believe that these two images are a little further apart than those two images, and so the person is maybe increasing their speed. If all the deltas were exactly the same, the spacing was exactly the same, then we would say constant speed. All right. How do we deal with motion diagrams? You don't have to draw images over and over again. It gets a little cumbersome. Just make it a dot. Person at time 1. Person at time 2. Time 3. Time 4. And time 5. And then, if we give you some numbers here, it's going to make good sense. Let's say this is 10 meters. This is 20 meters. This is 30 meters. And this is 40 meters. And each interval corresponds to one second. Okay. So there is one second in between each flash of our camera. All right. So now based on these numbers, you would probably say, oh, the person is running at constant speed. They are going 10 meters in the first second. They've gone 20 meters in two seconds, 30 meters in three, and 40 meters in four, which is running at 10 meters per second, which maybe some of you guys can do. I know for a fact that at my advanced age I cannot do that, all right, but 10 meters per second, that's moving. All right. How do we make this into a motion diagram that looks like this? X versus T? Well, we have T, T is zero and then 1 second, then 2 seconds, then 3 seconds, then 4 seconds. So I need one, two, three, four marks right there. And we have the x measurements. So x equals 10 and then x equals 20. And then x equals 30, and then x equals 40, and then we, of course, get a straight line that connects all those. So in this example, this is what the graph would look like. This is the position versus time graph, x versus t. And that actually has a lot of information in it. Because now, looking at this graph, are they moving at constant speed or are they increasing their speed or decreasing their speed? >> (student speaking) Constant. >> Constant speed, right? Constant speed the whole way. If they are moving along at constant speed, or more specifically, constant velocity, what is their acceleration? >> (student speaking) Zero. >> Zero. Zero acceleration. One graph actually has a lot of information. It tells us about the position. But it also tells us about the velocity as a function of time, and it tells us about the acceleration as a function of time. So it's important to be able to plot these things, and make sense of them.