Question

A car travelling 19.4m/s passes apolice car at rest.As it passes, the police car starts up, accelerating with a magnitude of 3.2m/s. Maintaining that acceleration, how long will it take the police car to catch up with the speeding motorist?

Answer 1

A car travelling $19.4 \, \text{m/s}$ passes a police car at rest. As it passes, the police car starts up, accelerating with a magnitude of $3.2 \, \text{m/s}$. Maintaining that acceleration, how long will it take the police car to catch up with the speeding motorist?

Suppose an initial moment police car located at point $x = 0$. Then its coordinate equals:

$$S_p = \frac{a t^2}{2}$$

a – acceleration of police car

t – time

And coordinate of car equals:

$$S_c = v t$$

v – speed of car

Police car catch the car then $S_p = S_c$:

$$\frac{a t^2}{2} = v t$$ $$\frac{a t}{2} = v \quad \Rightarrow \quad t = \frac{2 v}{a}$$ $$t = 2 \cdot \frac{19.4}{3.2} = 12 \frac{1}{8} = 12.1 \, \text{s}$$

Answer: 12.1 seconds.