Question

A thief passes a policeman at a velocity of 15 m/s. The police car starts chasing with acceleration of $2m{s}^{-2}$. Find the time taken by the policeman to catch the thief if the police car started from rest.

Answer 1

Given,

The velocity of the thief = 15 m/s

Acceleration of the policemen = $2m{s}^{-2}$

Initial velocity of the policeman is 0

Let the police catch the thief after t second.

Now,

Distance traveled by thief = 15t

Distance traveled by policeman

$s=ut+\frac{1}{2}a{t}^2$

Or, $s=0+\frac{1}{2}\times 2\times t^2$

Or, $s=t^2$

When the policeman catches the thief the distance traveled will be equal

So,

$15t=t^2$

$Or,t=15s$

Hence the policeman will catch the thief after 15 seconds.