A police car at rest, passed by a speeder traveling at aconstant 120 km/h, takes

Question

A police car at rest, passed by a speeder traveling at aconstant 120 km/h, takes off in hot pursuit. The police officer catches up to the speeder in 750 m,maintaining a constant acceleration. (a) Qualitatively plotthe position vs. time graph for both cars from the policecar’s start to the catch-up point. Calculate (b) howlong it took the police officer to overtake the speeder, (c)the required police car acceleration, and (d) the speed of thepolice car at the overtaking point. A police car at rest, passed by a speeder traveling at aconstant 120 km/h, takes off in hot pursuit. The police officer catches up to the speeder in 750 m,maintaining a constant acceleration. (a) Qualitatively plotthe position vs. time graph for both cars from the policecar’s start to the catch-up point. Calculate (b) howlong it took the police officer to overtake the speeder, (c)the required police car acceleration, and (d) the speed of thepolice car at the overtaking point.

Explanation / Answer

a) the graph for the speeder is a straight line and for the police caris parabola with increasing slope. b) time required by the police officer to overtake the speederis time required by the speeder to travel the distance of 750mbecause both of them travels the same distance in same time; so T=750/(120*1000/3600)=22.502s. c) u=0; t=22.502s; S=750m; S=ut+1/2at2; putting the values we get: a=750*2/(22.502*22.502)=2.962m/s2. d) v-u=at; v=2.962*22.502=66.66m/s.

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