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A Moving Car

Patrick Ford
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Hey, guys, hopefully you give this one a shot. We're gonna get some more practice with position diagrams, but take a look at this example together, we have a position diagram for a moving car. We've got points a through E. Let's just start with the first one. Where is the car moving the fastest. So again, we're just going to stick to the steps. Which variable are we talking about? Position, Velocity or acceleration? What? We're talking about motion here. Where we moving the fastest. So it's not gonna be the position. And remember, acceleration is a change in motion. So we're actually not gonna talk about acceleration either. It's gonna be the velocity. So that's the first step. Now the now the graph feature. We just get by using the table down here when we're looking at a position Time diagram. We are looking for the velocity. So that means we're gonna look at the slopes of the graph. There's a couple of rules to remember. Remember that upward slope? They're gonna be positive flat zero. And the negative is downward or downward is negative and steeper you are, the faster you're going. So that's the That's the rule that we're gonna use. So we're looking for the slopes here, So that's the second step. The third one is the qualifier. So the qualifier, in which of these terms over here in this list are we gonna use? Well, the fastest is the key word here. The fastest means like the most where you're moving the most fast. So in this list, that's actually gonna be the maximum value over here. So that's the third step. We figured out that we're looking for the maximum slope. Notice how the question also doesn't say forwards or backwards anything like that. So we're actually looking for here. Remember, maximum slopes are gonna be the steepest slopes, and it doesn't matter whether it's upward or downward. We're just looking for the most vertical slope. So now we just have to interpret from the graph. And to do this, we actually have to draw out the slopes for each of these points. So let's just go ahead and quickly do that by looking at the the tangent lines. That is gonna be the slopes. Treat each of these points. Now I just have to figure out which one of these points is the steepest. If you take a look, that's actually just gonna be point C. So that's our answer. Moving on to the second one. Where is the moving the slowest again? Guys, if you go through all the steps, we're moving the slowest means we're gonna talk about velocity. We know that means we're looking at the slopes. So now for the qualifier. Well, if the fastest meant we were looking at the maximum, then the slowest means we're just gonna look for the minimum. And so if the steepest slope was the maximum, the flat ist slope is gonna be the minimum. So let's get the graph. Where do we have flat slopes? Well, it's actually pretty easy at point B and appoint d. We have flat slopes, so those are gonna be points B and D. There's actually also are where you have no motion at all. It's V equals zero. So if you're not moving, that's the slopes, Ugo. So now move on to part three. Where is the car turning around? So what does this mean? What is turning around mean? Well, if you turn around, you're gonna be moving in one direction. You stop and then you move in the other direction. So we're still talking about motion. Here's which. Which position? Sorry, which variable we're gonna use. We're gonna use the velocity. So we're talking about velocity, Which means we're gonna talk about this slope. Those are the first two steps, and now we just have to look at the qualifier. So which one of these in this list is gonna be the right qualifier? Well, again, remember what turning around means means you're moving in one direction and then you turn around and you move in the opposite direction. You're talking about a change in direction. And so remember, when you're talking about the slopes, when you have upward slopes, that's gonna be positive velocity. That means you're moving forward. Downward slopes is gonna be negative velocity, which means you're moving backwards. So when you're looking for a direction change, where you're actually looking for is a sign change. That's the qualified we're gonna use when you use a sign change. So now we just have to interpret from the graph at point A. Because it's upward. You have a positive velocity point B, you have the equal zero, and then point see because it's downwards. You have negative velocity. Which means somewhere inside of this little point over here you are going forwards. You stopped and then you turned around and started moving backwards. That actually happens Very like right here at point B. It happens when you stop momentarily and then right before you start moving in the backwards or opposite direction. So that means that happens at B. Now, is there any other point? Well, at D were also the equal to zero. But what happens is it's a constant zero for a long time. There is no change or to flip in the sign so d is not a turning point here. Okay, so that's it. Now for the last two, where is the car speeding up and slowing down? So let's just go thru are variables Which are we talking about? Position, velocity or speed or acceleration? Well, you might think Oh, we're talking about speed, so we're gonna be looking at speed. But actually, what's happening is speeding up means the speed is increasing its talking about a change in that speed. So we're actually gonna be talking about the acceleration here. So that's the first step Now we just have to figure which graph feature we're talking about again going down to our table. We're gonna see that when we talk about the acceleration in the next a graph. We're looking at the curvature and there's a couple of rules to remember when we have a smiley face upwards like this, that's gonna be positive. Acceleration of frowny face is gonna be negative acceleration. And then also we have to remember is we have to remember that if you break up these smiley faces in frowny faces into two halfs, then on the left side you're always going to be slowing down. So in these pieces right here, you're going to be slowing down. Because as you move towards the center, your slopes are becoming more flat, which means you're sort of going to zero. Whereas on the right side, your slopes are becoming more vertical on here. So you're actually going to be speeding up? That's what you need to remember. So left is slowing down and right is speeding up. So let's go back to the question we're gonna you know, we're gonna be looking at the curvature over here for speeding up for the acceleration. So which qualifier makes the most sense? Well, this is the only case where the qualifier doesn't really make a whole lot of sense. Uh, there's no really good choice that we can pick from this from this table That will help us here. Instead, we're gonna use this rule that we talked about about speeding up and slowing down. So here we're gonna go to the graph, figure out all the places where you have curvature. So, for instance, right here and also at E. We also have, like, another sort of half smiley face, and then we just break up each curve into two halves. So just break this up into two halves and this one's already kind of a half, and then we're looking at speeding up. That's just gonna be any points to the rights of those curves. So, for instance, at sea where that's gonna be to the right of the curve and also an e. This is also to the right of the curve, So C and E are our choices for speeding up. You can also tell because the slopes of these lines are becoming mawr vertical as you move along here. All right. So finally, the last one, where we slowing down guys, that's just gonna be the opposite. We know we're looking at acceleration, which means we're looking at the curvature. And so now, instead of looking for the right sides of those curvature, is we're just gonna be looking at the left sides. So the left is when we're is when we're slowing down, The only point that fits here is actually gonna be point a again. Remember, this is sort like a half. Uh, this is like a half smiley. It's not really a full one, so d doesn't count. So that means that point is our answer choice, and that's it. Let me know if you guys have any questions.