Curved Position-Time Graphs & Acceleration

by Patrick Ford
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Hey, guys. So sometimes you're gonna see position time graphs that are curved like this instead of just a bunch of straight lines. So in this video, I'm gonna show you the differences between these two types of position graphs because there's a few conceptual points that 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, and what that means is that the velocity is changing. And so what that means is that the acceleration is not equal to zero. Let's check it out when we have these kinds of straight lines in position graphs. Basically, what that means is that between any of the 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 gonna get the same value, which means that the acceleration is equal to zero. 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 zero. And that's because if you take any two points on this graph, for instance, these two points. Then we can see that this slope is constantly going to be changing. It's gonna go from here to here to here. And so the slope or the velocity is changing means that there is some acceleration. So there's a couple things you need to know about this acceleration. The first one is the sign of the acceleration. And so there's a really simple rule whenever the the position time graph is curving up. So I like to think about it like a smiley face like this, that what that means is that the acceleration is positive. So this is a positive acceleration in one way you can think about this is that the slope over here in this first half is downwards, which means it's gonna be a negative velocity just to 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 two, a positive number that can Onley 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 gonna have a left side and a right side. So in this left side of here, um, the object is always going to be slowing down. And that's because if you think about this this the velocity in this first section here is gonna be steep. It's gonna be really, really vertical. And then when you get over here, the velocity starts becoming more flat, more horizontal like this. So you're gonna be slowing down because your velocity gets closer to zero on the opposite, 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. It's because now you're the slope of this line. It's the slope between any two points is now going to get Mawr and Mawr vertical, which means the magnitude gets bigger. Alright, guys, that's really all you need to know about these kind of graphs. Lett's Let's move on.