Question

A car is travelling at a constant speed of 670m/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 70m/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

$$\frac{at^2}{2}=v(t+1),$$

$$\frac{70t^2}{2}=670(t+1),$$ $$t^2-19.1t-19.1=0,$$ $$t=20\:\rm s.$$

Finally, the distance traveled by trooper

$$d=\frac{at^2}{2}=\frac{70\times 20^2}{2}=14000\:\rm m.$$