A police car waits in hiding slightly off the highway. A speeding car is spotted by the police car doing 40 m/s. At the instant the speeding car passes the police car, the police car accelerates from rest at 4 m/s2 to catch the speeding car. How long does it take the police car to catch the speeding car

t = 20s

Explanation:

In order for the police car to capture the other car, both cars must travel the same length.

The distance traveled by the first vehicle is:

S = ^ Vt = 40t, where t represents the elapsed time and V the vehicle speed.

The distance traveled by the police car is:

S = at ^ 2/2 = 2t ^ 2, where t represents the elapsed time, a is the acceleration of the car.

As the distances traveled are equal:

40t = 2t ^ 2 in this way t = 20s