A woman is running at 5.1 m/s to catch a bus parked at the bus stop. When she is 11 m from the bus, the bus leaves the stop with an acceleration of 1 m/s² (away from the woman). The latest (longest) time at which the woman can catch the bus is A) 3 seconds. B) 4 seconds. C) 7 seconds. D) 8 seconds.

Question

Quizplus · Accepted Answer

The woman and the bus will have the same position when the time is 7 seconds. The woman's position is given by $ x_w = 5.1t $ and the bus's position is $ x_b = 0.5t^2 + 11 $. Setting $ x_w = x_b $ and solving for $ t $ gives $ t = 7 $ seconds.

A Woman Is Running at 5