A policeman on a motorcycle is stopped at a speed trap. A car is moving at a con

Question

A policeman on a motorcycle is stopped at a speed trap. A car is moving at a constant velocity of 100 mph along a straight stretch of road as he passes the policeman at a constant rate of 3 m/s each second. (a) How long does it take the officer to catch the driver? (b) How far does the police officer travel in that time? (c) How fast is the motorcycle traveling when the policeman reaches the speeding car? (d) Plot the position of the policeman and the position of the car vs. time on the same graph. (e) Plot the velocity of the policeman and the velocity of the car vs. time on the same graph.

Explanation / Answer

1. speed of car = 100 mph = 160 km/h = 44.4 m/s

acceleration of policeman = 3 m/s2

initially at speed trap the police vehicle is at rest

so initial velocity u =0

Let t be the time after which the po;oceman catches the car

so 44.44 *t = 0.5 * 3 * t^2 : dist travelled by car and bike will be same when the police catches the thief

t = 29.26 s

2. distance travelled = 44.44* t = 1166m = 1.16km

3. final speed of motorcycle = a*t = 3*29.26 = 87.78 m/s

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