Question

a car is taveling at 80 km/hr in a school. A police car is at rest in the parking lot of the school. It takes the policeman 0.5 sec to react before he begins accelerating after the speeder with an acceleration of 8 m/sec square. A) how far has each car traveled when the police car catches the speeder B) how fast is the police car going when it catches the speeder?

Answer 1

Given velocity of car , V_c = 80km/hr * 5/18 = 22.22 m/s

Initial velocity of policeman = 0 , acceleration, a_p= 8 m/s²

Police man takes 0.5sec to react after car started,

So, Distance covered by car in 0.5sec , d1 = vt = 22.22*0.5 =11.11 m and d2 = 22.22t => D = 11.11+22.22t

When police starts car is already 11.11 m ahead of it.

Distance covered by police,D = 1/2at² = 0.5*8*t² = 4t²

Velocity of police, v_p = at = 8t

But D is same for both => 4t² = 11.11+22.22t => t = 6 sec

So, D = 4*6² = 144 m

Velocity of police, v_p = at = 8t = 8*6 = 48 m/s