Single Variable Calculus Questions and Answers

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Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 12

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The graph of the position function of two runners $A$ and $B$ is shown below. Suppose that the runners finish a 100$m$ race in a tie.

a.) Describe and compare how the runners run the race.

Based from the graph, the runner $A$ finishes the race with a constant speed while runner $B$ has changing speed.

b.) When is the time where the distance between the runners is greatest?

Based from the graph, the time where the distance between the runners is greatest, is approximately at $t = 5$ seconds.

c.) At what time do the runners have the same velocity?

Based from the graph, the time where the runners have the same velocity is at $t = 0 $ and $t = 14 $ seconds.