Question

A car is travelling at a constant speed of 72 / km h and passes a stationary
police car. The police car immediately gives a chase, accelerating uniformly to
reach a speed of 90 / km h in 10 seconds. And continues at this speed until he
overtakes the other car. Find;
(i) The time taken by the police to catch up with the car,
(ii)The distance travelled by the police car when this happened.

Answer 1

We have

$$s_1=s_2\to v_1t=v_2(t-T)+0.5v_2T$$

a)

$$\frac{72}{3.6}t=\frac{90}{3.6}(t-10)+0.5\frac{90}{3.6}10$$

$$t=25\ s$$

b)

$$s_2=s_1=\frac{72}{3.6}25=500\ m$$