posted by Ralph .
a police car is cruising on the right lane at 25 m/s (meters/sec.). A motorcycle, on the left lane, passes the police car at a constant 35 m/s. The police officer reacts fast and accelerates at a constant 5 m/s^2.
(a)When does he catch up?
(b)What was his velocity at that instant?
At the time t after the police car is passed, the distances travelled are:
X1 (motorcycle) = 35 t (meters)
X2 (police) = 25t + (1/2)(5)t^2
(a) Set X1 = X2 and solve for t. Ignore the t=0 solution. Take the other one.
(b) V2 = 25 + 5t is the celocity of the police car. Use the appropriate value of t.