Question

Robbers in a car travelling at 20 m/s pass a policeman on a motor cycle at rest.The policeman immediately starts chasing the robbers.The policeman accelerates at 3 m/s² for 12 s and thereafter travels at a constant velocity .Calculate the distance covered by the policeman bfore he overtakes the car ?

Answer 1

Suppose after time, t policeman overtakes the car.

Also, distance covered by both car and motor cycle is same, x(say).

For robber,

v =x/t

=> 20 = x/t

=> x = 20t .......................(1)

For policeman,

for first 12s, u =0

v =0+ 3*12 = 36m/s.

s = 0 + 0.5*3*12*12

=> s = 216m

for time, t

x = s + 36*t' = s +36(t - 12)

=> 20t = 216 +36t - 432 (using eqn. 1)

=> 16t = 216

=> t = 13.5s

So, x = 20*t = 20* 13.5 = 270m.