Question

Two runners start one hundred meters apart and run toward each other. Each runs ten meters during the first second. During each second thereafter, each runner runs ninety percent of the distance he ran in the previous second. Thus, the velocity of each person changes from second to second. However, during any one second, the velocity remains constant. Make a position-time graph for one of the runners. From this graph, determine (a) how much time passes before the runners collide and (b) the speed with which each is running at the moment of collision.

Answer 1

The two runners start one hundred meters apart and run toward each runs ten meters during the first second and, during each second thereafter, each runner runs ninety percent of the distance he ran in the previous second. While the velocity of each runner changes from second to second, it remains constant during any one second.

a)

Since the two runners are running toward each other in exactly the same way, they will meet halfway between their respective starting points. That is, they will meet at x = 50.0 m. According to the graph, therefore, this position corresponds to a time of 6.6 s.

b)

Since the runners collide during the seventh second, the speed at the instant of collision can be found by taking the slope of the position-time graph for the seventh second. The speed of either runner in the interval from t = 6.00 s to t = 7.00 s is