Two balls roll along the paths shown above. The position of...

Two balls roll along the paths shown above. The position of the balls is shown at equal time intervals of one second each. When does Ball B have the same speed as Ball A. Ball A t = 0s t = 1s t = 2s t = 3s t = 4s Ball B t = 0s t = 1s t = 2s t = 3s t = 4s (1) t = 1.0 sec (2) t = 1.5 sec (3) t = 2.0 sec (4) t = 2.5 sec (5) t = 3.0 sec

Transcript

00:01 So in this problem we want to look at velocity as it relates to position and time.

00:08 So we have the snapshot of the ball at each time, t is equal to 0 seconds, then 1, 2, 3, 4 seconds, and this is ball a.

00:21 Now what is the definition of velocity? well the velocity, and here we're going to look at the average velocity, the average velocity is defined as the change in position over the change in time.

00:34 As opposed to the calculus definition where it's the derivative of position with respect to time, but we have a finite difference here so we should use this definition.

00:43 Now we have a change in x here, delta x, and then we have a change in time.

00:51 So for ball a here, what's our average velocity? well it's whatever change in x is over the change in time, and the delta is the final minus the initial state, so basically the velocity is delta x meters per second if this is in, say, meters, and then we have seconds of course.

01:10 Now for ball a we see these are all the same exact term here, so they all have the same delta x.

01:18 These are all 1 second intervals, which means the velocity average here, or velocity a, is constant.

01:26 So that's the first thing we should see because we have equally spaced images here.

01:33 Now ball b is a little different, and it's going to be a little difficult to draw these, but i'll do the best i can to draw them in order.

01:45 Again, 0, 1, 2, 3, 4 seconds, and do this comparison on your paper to get it a little more accurately.

01:55 Now if we try to draw the same length delta x, it's maybe about like that, and so what's that tell us about the velocity here? the velocity here is greater than our va, because we have a 1 second change in time still, but the change in x is much greater if these two pictures are to scale.

02:23 Now consequently let's look at, say, the other one here, and that looks pretty even as a delta x.

02:32 Now our delta x here for vb is less than va, because our delta x for vb is less, because we have the va term here, and so the velocity therefore is less because we have the same time.

02:45 So what we want to look for is to finally point to where v, the point to where v has the same velocity, is look for this region where we have the same delta x, and it looks like it is here, because we can draw through and see that between 2 and 3 delta x is about the same...

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