Question

A car is travelling at a constant speed of 950m/s. Passes a trooper hidden behind a Billboard one second of the car passes the Billboard, the trooper sets out from the Billboard to catch it, acelerating at a constant speed of 100m/s².how long does it take her to take the car?

Answer 1

Let the time of motion of the trooper is t, then distance traveled by her

$$d=\frac{at^2}{2}.$$

The distance traveled by a car

$$d=v(t+1).$$

Hence

$$\frac{at^2}{2}=v(t+1),$$ $$\frac{100t^2}{2}=950(t+1),$$ $$t^2-19t-19=0,$$ $$t=20\:\rm s.$$

Finally, the distance traveled by trooper

$$d=\frac{at^2}{2}=\frac{100\times 20^2}{2}=20 \:000\:\rm m.$$