Problem 2-99 - v-t graph

Two cars, \(A\) and \(B\), are stopped for a red light beside each other at an intersection. The light turns green and the cars accelerate. Their velocity time graphs are shown in the figure below. (The positive direction is "forward.")

graph indicating car A and car B accelerating

(a) At what time(s) do \(A\) and \(B\) have the same velocity?
(b) When does \(B\) overtake \(A\)? (Hint: Their displacements must be equal at that time and displacement can be found from a velocity time graph.)
(c) How far have the cars traveled when \(B\) overtakes \(A\)?

In a \(v\) vs \(t\) graph of the two moving objects they have the same velocity when:

(A)   The areas under the graphs are equal.

(B)   The slopes of the graphs are equal.

(C)   The graphs cross each other.