Question

A police car moving at $60m{s}^{-1}$ is pursuing a minivan moving at $45m{s}^{-1}$. How long will it take the police car to catch up if the mini-van is $600m$ ahead of the police car at the beginning of the chase?

• A. $10\text{second}$
• B. $15\text{second}$
• C. $40\text{second}$
• D. $50\text{second}$

Answer 1

The correct option is C $40\text{second}$

Given:
Speed of the police car: $v_p=60m{s}^{-1}$
Speed of the minivan: $v_m=45m{s}^{-1}$.
Mini-van is $600m$ ahead of police.

Let the time taken by police car to catch the mini-van be $t$.

Distance is equal to the product of speed and time.
Distance travelled by police car is:
$s_p=v_{p}t$
$s_p=60t$

Distance travelled by mini-van is:
$s_m=v_{m}t$
$s_m=45t$

Distance travelled by police car $\left(s_p\right)$ is 600 m more than distance travelled by mini-van $\left(s_m\right)$.
$s_p=s_m+600$
$60t=45t+600$
$t=40s$