A speeder traveling at a constant speed of 34.7 m/s races past a stopped patrol

Question

A speeder traveling at a constant speed of 34.7 m/s races past a stopped patrol car on the interstate. A patrol car pursues from rest with constant acceleration of 2.22 m/s2 until it reaches its maximum speed of 52.8 m/s, which it maintains until it catches up with the speeder. Both cars are always traveling west on the interstate.

a)How long does it take the patrol car to reach a speed of 52.8 m/s if it starts moving just as the speeder passes?

b)How long does it take the patrol car to catch the speeder if it starts moving just as the speeder passes?

c)How far does each car travel during the period when the parol car starts moving till it catches th espeeding car?

Explanation / Answer

a) v=at

=> t = 52.8/2.22 = 23.78s

b) distance travelled by speeder = 34.7t

disance travelled by police car = 52.8t-0.5*2.22*t*t

as the both are equal so :-

52.8t-0.5*2.22*t*t = 34.7t

=> t = 49.61s

c) distance travelled = 34.7*49.61 = 1721.47m

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