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# Shown are graphs of position functions of two runners, $A$ and $B$, who run a 100-meter race and finish in a tie.(a) Describe and compare how the runners run the race.(b) At what time is the distance between the runners the greatest?(c) At what time do they have the same velocity?

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So in this problem, we are given a graph the position of two runners and be Running 100 m race. And the graph looks something like this mm brass to describe and compare how the runners run the race. Well, we can see that, first of all, runner A right is at a constant velocity, right? They run the race the constant speed or velocity or we could say pace. Okay, Runner B starts slow and then what the slope here is really small to start off with. Right, And then what happens? It gets real steep toward the end. So then mm they steadily feet out to catch up. Okay, now, the next question is, at what time is the distance between the runners? The greatest. So, we're trying to figure out in here at what time is this distance between these two curves? The greatest. Right. Well, you can see my looking at the graph here, right, it looks like that. Right? Here, we have the greatest distance between the two curves. So, for part B we could say at eight seconds. All right. We have the greatest distance between the two curves. Mhm. Okay, No question C. Is at what time do they have the same velocity? All right. So, if we look at the slopes here, right, well, the slope of A is the same all the way through. Let's look at the slope of B here, it's real small here, it seems to be going straight up like that. And then here it's really steep. Right on up the slope is And if you notice it looks like around eight seconds that the velocity for A and the velocity for B. E. Are in parallel. So again, You could say at eight seconds that they seem to have the same slope for the same speed, same velocity.

DM
Oklahoma State University

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