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 12 secs and travels at a constant velocity. calculate the distance covered by policeman before he overtakes the car

Answer 1

Hey Friend !

Speed = Distance/ Time

Distance = Speed x time

Speed of the robbers' vehicle = 20m/s
Time = t

Distance traveled by robbers = s =  20t

Initial velocity = u


Distance traveled by police [ 12 sec ] = s = ut + 1/2at²

Initial velocity [ starting from rest ] = 0

acceleration = a = 3m/s²

Time = t = 12 sec

s = 0 + 1/2 × 3 × 12 × 12
   = 216 metres 
Velocity of the police car[final velocity ] = v = u + at
                                                         = 0 + 3 × 12
                                                        = 36 m/s

Distance traveled by the robber after 12 sec will be = s
            = 36(t - 12) metres
            = 36t - 36 x 12
            = 36t - 432 metres

Total distance traveled by robbers before being chased = Total distance traveled by police
              = 36t - 432
              = 20 t

20t = 36t - 432

432 = 36t - 20 t

432 = 16t

t = 432 / 16

t = 27 sec

Distance traveled by police  = 20t = 20 x 27 
                                             = 540 metres