Question

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

Answer 1

Here, u=0,t=12 sec , a=3 m/s²

Distance covered by the policeman in 12 seconds is:-

We know that,

s=ut + 1/2at²

→0×12 +1/2(3)(12)²

→1/2(3)(144)

→3×72

→216 m

v = u +at

→0 + 3(12)

→36 m/s

The distance covered by the robber in 12 seconds is :-

Distance = speed × time

→20 m/s × 12 s

→240 m

Suppose the policeman overtakes in 12+t seconds

Then distance = 216 + 36t

Then distance covered by the robber in the same time is

→Speed × time = 20 ( 12 + t )

216 + 36 t = 240 + 20 t

36t-20t = 240-216

16t = 24

t = 24/16

t = 3/2 = 1.5 seconds

the distance covered by the policeman before he overtakes the car in 12 + 1.5 = 13.5 seconds is

216+36t

→216 + 36(1.5)

→216 + 54

→270 m