Question

A motorist travelling with a constant speed 15m/s passes a school crossing corner where speed limit is 10m/s just as the motorist passes a police on a motorcycle starts off in pursuit with a constant acceleration 3m/s2 .How much time elapses before he catches up with the motorist?

What is the officers speed? What is the total distance travelled byveach vehicle at that point?

Answer 1

(a) The distance traveled by the motorist can be found as follows:

$$d_1=v_0t=15t.$$

The distance traveled by the police on a motorcycle can be found as follows:

$$d_2=\dfrac{1}{2}at^2=1.5t^2.$$

When the police on the motorcycle catches up with the motorist, $d_1=d_2$:

$$15t=1.5t^2,$$ $$t=\dfrac{15\ \dfrac{m}{s}}{1.5\ \dfrac{m}{s^2}}=10\ s.$$

(b) We can find the officer's speed as follows:

$$v=v_0+at=0+3\ \dfrac{m}{s^2}\cdot10\ s=30\ \dfrac{m}{s}.$$

(c) We can find the total distance travelled by each vehicle at that point as follows:

$$d=v_0t=15\ \dfrac{m}{s}\cdot10\ s=150\ m.$$