A car passes a point A A\,A on a straight horizontal road with speed 30 m s−1^{-1}−1, moving with constant deceleration 1.5 m s−2^{-2}−2.
At the same instant a motorcycle starts from rest at A A\,A and moves along the same road in the same direction with constant acceleration 2.5 m s−2^{-2}−2.
Show that the motorcycle draws level with the car 15 seconds after they pass AAA.
Find the distance from A A\,A at which the motorcycle draws level with the car.
Show that, at the instant the motorcycle draws level with the car, the motorcycle is travelling 30 m s−1^{-1}−1 faster than the car.