Answer to Question #94670 in Mechanics | Relativity for Jazzmeyn

Question

A speeding car is travelling at a constant speed of 25m/s when it passes a stopped Car. If the police are accelerates at 6m/s squared how far will the police car have travelled when it catches the speeding car

Answer 1

The equation of motion of a speeding car

$$x_{1}=vt=25t$$

The equation of motion of a police car

$$x_2=\frac{at^2}{2}=\frac{6t^2}{2}=3t^2$$

When a police car catches the speeding car

$$x_1=x_2$$

So

$$25t=3t^2$$

$$t=\frac{25}{3}\:\rm s=8.3\: s$$