Anderson Video - Motion Diagram of Accelerating Car

Professor Anderson
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 Hello class, Professor Anderson here. Let's take a look at an example of your car accelerating in terms of these motion diagrams and see if we can figure out how to plot this out. So let's say that your car is accelerating from a stop and then coming to rest. okay so the Okay, so the light turns green, you accelerate, you drive for a little while and then the next stoplight you come back to a rest. So, what does the motion diagram look like for this car Well, motion diagrams are of course a series of dots and let's imagine that each dot or each frame corresponds to one second. Okay, here we are at position one. As we accelerate our car position is going to increase like so and then as we come to a stop, the position starts to— the interval I should say get smaller and smaller and smaller. Okay, and so maybe it looks like this right the position is going to the right, the displacement is to the right, the Delta X between each segment is small gets big and then get small again. All right and let's try this for some real numbers and let's see if we can plot it out so we will start here at x equals zero and we will increase to the right like we typically do and let's just pick some arbitrary values, okay. So, the first one here— we're going to move this over a little bit just to align with that. The first one here is at x equals zero the next one is at x equals ten meters. We'll use meters just to be fair. And now we've jumped up to 30 meters and now this is even a little bit further than that, 60. And now we go a little bit further, maybe a hundred and now we're moving at roughly the same clip so the difference here— sixty to a hundred is 40, so this would be one hundred and forty, this would be a hundred and eighty, this would be two hundred and twenty, and now we're starting to slow down. And so in each time interval, our Delta X isn't quite as far anymore so maybe this is more like thirty again. So, 220 plus 30 is 250. And now this is maybe like 20. So this would be 270 and maybe this is more like 10, so that's 280 and now we really start to sort of slow down rather quickly. This is maybe 285, 288, 289. And let's just pick an ending point we'll say it's 290. All right a lot of data points here for motion. How are we going to plot X as a function of time? Well it's not too bad right because we have all the data and what we said was each interval is one second. So let's just count the number of dots. We've got 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 and so we need 15 little markers here: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. Alright, we start at 0. Then we go to position 10. Then we go to position 30. Then we go to position 60. Then we go to position 100 and now we go to a position 140 and so forth and you can see right off the bat we're going way too steep we're going to run out of room on our graph. So let's try it again we'll go a little bit more shallow, okay. Let's say that this is the ending point 290, all right, which means that this is roughly 200, this is 100, something like that. All right, so 10 would be about there, 30 is the next point, 60 is the next point 100 is at that point right there. All right, and then we go 140, 180, 220 250 270 280 288 289 290 All right, this is what our motion would look like. It's a series of points of course since we had data that was individual numbers but to aid the eye we can draw a line. Accelerating, constant speed, decelerating. Something like that okay. These are called motion diagrams and to help you think about visualizing these cases and putting it on a graph. All right, hopefully that is clear. If not come see me during office hours. Cheers
 Hello class, Professor Anderson here. Let's take a look at an example of your car accelerating in terms of these motion diagrams and see if we can figure out how to plot this out. So let's say that your car is accelerating from a stop and then coming to rest. okay so the Okay, so the light turns green, you accelerate, you drive for a little while and then the next stoplight you come back to a rest. So, what does the motion diagram look like for this car Well, motion diagrams are of course a series of dots and let's imagine that each dot or each frame corresponds to one second. Okay, here we are at position one. As we accelerate our car position is going to increase like so and then as we come to a stop, the position starts to— the interval I should say get smaller and smaller and smaller. Okay, and so maybe it looks like this right the position is going to the right, the displacement is to the right, the Delta X between each segment is small gets big and then get small again. All right and let's try this for some real numbers and let's see if we can plot it out so we will start here at x equals zero and we will increase to the right like we typically do and let's just pick some arbitrary values, okay. So, the first one here— we're going to move this over a little bit just to align with that. The first one here is at x equals zero the next one is at x equals ten meters. We'll use meters just to be fair. And now we've jumped up to 30 meters and now this is even a little bit further than that, 60. And now we go a little bit further, maybe a hundred and now we're moving at roughly the same clip so the difference here— sixty to a hundred is 40, so this would be one hundred and forty, this would be a hundred and eighty, this would be two hundred and twenty, and now we're starting to slow down. And so in each time interval, our Delta X isn't quite as far anymore so maybe this is more like thirty again. So, 220 plus 30 is 250. And now this is maybe like 20. So this would be 270 and maybe this is more like 10, so that's 280 and now we really start to sort of slow down rather quickly. This is maybe 285, 288, 289. And let's just pick an ending point we'll say it's 290. All right a lot of data points here for motion. How are we going to plot X as a function of time? Well it's not too bad right because we have all the data and what we said was each interval is one second. So let's just count the number of dots. We've got 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 and so we need 15 little markers here: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. Alright, we start at 0. Then we go to position 10. Then we go to position 30. Then we go to position 60. Then we go to position 100 and now we go to a position 140 and so forth and you can see right off the bat we're going way too steep we're going to run out of room on our graph. So let's try it again we'll go a little bit more shallow, okay. Let's say that this is the ending point 290, all right, which means that this is roughly 200, this is 100, something like that. All right, so 10 would be about there, 30 is the next point, 60 is the next point 100 is at that point right there. All right, and then we go 140, 180, 220 250 270 280 288 289 290 All right, this is what our motion would look like. It's a series of points of course since we had data that was individual numbers but to aid the eye we can draw a line. Accelerating, constant speed, decelerating. Something like that okay. These are called motion diagrams and to help you think about visualizing these cases and putting it on a graph. All right, hopefully that is clear. If not come see me during office hours. Cheers