Hey, guys. So sometimes you're going to see position time graphs that are curved like this instead of just a bunch of straight lines. In this video, I'm going to show you the differences between these two types of position graphs because there are a few conceptual points you need to know. Let's check it out. So, guys, whenever you see a position time graph that is curved, not a bunch of straight lines, then what that means is that the velocity is changing. And so what that means is that the acceleration is not equal to 0. Let's check it out. When we have these kinds of straight lines in position graphs, basically, what that means is that between any two sections, the velocity is constant. So if I take the slope between this line, between any two points on this line here, I'm just going to get the same value, which means that the acceleration is equal to 0. But when you have curvature in your position graphs, when these things look like squiggly lines or curves, what that means is that the acceleration is not 0. And that's because if you take any two points on this graph, for instance, these two points, then we can see that the slope is constantly going to be changing. It's going to go from here to here to here. And so the slope or the velocity is changing means that there is some acceleration. So there are a couple of things you need to know about this acceleration. The first one is the sign of the acceleration, and there's a really simple rule. Whenever the position time graph is curving up, like a smiley face like this. Then what that means is that the acceleration is positive. One way you can think about this is that the slope over here in this first half is downwards which means that's going to be a negative velocity, just a sign. And then from here to here in the second half, now, the velocity is positive. So we have the velocity that goes from a negative number to a positive number; that can only happen when there is positive acceleration. And then basically, the opposite is true for the other type of graph. So when you have curvature that's downwards, like a frowny face like this, then what that means is that the acceleration is negative and it's basically the opposite reasoning. First, it's going positive and then the velocity becomes more negative. Now the other thing that you need to know about curves is that we can always split curves sort of down the center like this. Curves are always going to have a left side and a right side. So in this left side here, the object is always going to be slowing down. And that's because if you think about this, this is the velocity in this first section here is going to be steep. It's going to be really, really vertical. And then when you get over here, the velocity starts becoming more flat, more horizontal like this. So you're going to be slowing down because your velocity gets closer to 0. On the opposite side, on the right side of the curves, no matter which one it is, whether it's a smiley or frowny, the object is going to be speeding up. And it's because now the slope of this line, the slope between any two points is now going to get more and more vertical, which means the magnitude gets bigger. Alright, guys. That's really all you need to know about these kinds of graphs. Let's move on.
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Position-Time Graphs & Velocity
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