Question

A car is travelling at a constant speed of 45m/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, accelerating at a constant speed of 3m/s².how long does it takes her to overtake the car. Draw the digram of this question

Answer 1

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

$$d=0.5at^ 2$$

 

The distance traveled by a car

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

$$v(t+1)=0.5at^2\to 45(t+1)=0.5(3)t^2$$

$$t=31\ s$$