Skip to main content
Pearson+ LogoPearson+ Logo
Start typing, then use the up and down arrows to select an option from the list.

Graph Velocity and Acceleration

Patrick Ford
Was this helpful?
Hey, guys, good to see you. Let's get some more practice with graphing all of these position, velocity and acceleration graphs. So we're gonna start from the origin were shown our velocity time graph. We're going to sketch the position and acceleration graphs. Let's just get to it. So we have the velocity time graph that's shown for us. And so if we're trying to get from the velocity to the acceleration and the position, I always like to start off with the acceleration first because I think it's the easiest. All we have to do is we just have to look at the slope of this line and what it's doing. So the slope of this line is constant and positive, and what that means is that we're gonna have a constant positive value for acceleration. So for this little piece right here, up until it gets to this point, the acceleration is just gonna have some positive value up until over here. But then what happens is that we have some changes, some abrupt change in sort of what the velocity graph is doing. So I've drawn this little like, dotted line here to sort of indicate that This is like a point where something happens in something changes here. So I'm gonna actually just gonna draw that all the way down the motion Over here. This dotted line. Okay, so now what happens is that instead of the velocity continuing to increase like it normally would. Now what happens is that we have it flipped, and now it starts to decrease. The velocity is now going down towards zero again. So that means that in this section right here, we have a negative constant slope, which means that we're gonna have a constant negative value for the acceleration. So that would look like, actually basically the same exact flat line. But it's now negative instead of positive. So there's some abrupt change here in the acceleration, and this is what it would look like. So that's the velocity and the acceleration. Now, what is the position? Time graph look like? The first question is where we're going to start in the first place and told we're told in text that we're gonna start from the origin, which means we're gonna start basically right from 00 So now, in order to get from the velocity to the position. We need to look at what the values are doing here. Now, the values for the velocity graph are actually going to be increasing right. The values are continuing to increase, which means that in the position graph, the slope is going to be increasing, so increasing values means increasing slope over here. So what that means is, if we have a increasing velocity, then that was gonna introduce, um, curvature. And again, we've already seen this piece right here. So now what happens in this section? Well, if increasing increasing values may increasing slope and what happens is decreasing values here, so decreasing values are going to result in a decreasing slope. So what would that look like? Would it look like this, or would it look like this or something like that? Well, the velocity is still going to be really high here, and then it's gonna eventually go down towards zero. So what happens is the velocity steepness is still going to continue on being the same. But eventually it's going to flatten out and become zero over here. So whenever this line here becomes flat, then that's going to corresponds to the velocity equaling zero on the graph. So that means that basically, it's gonna take this weird like s looking shape over here. And this is actually what the position time diagram would look like. Alright, guys, hopefully this sort of wraps this up. Let me know if you have any questions. That's it for this one.