Question

A Car travelling at a constant speed of 45.0m/s passes a highway patrol(HP) hidden behind a billboard. A second after the car passes the billboard the HP sets out to catch it, accelerating at a constant 3.00s. How long does it take to overtake the car?

Answer 1

Given:

$v=45.0\:\rm m/s$

$a=3.00\:\rm m/s^2$

The equations of motion of the cars

$$d_1=vt,\:\quad d_2=at^2/2$$

We get

$$d_1=d_2$$

$$vt=at^2/2$$

$$t=2v/a$$

$$t=2*45.0/3.00=30\:\rm s$$