A state trooper is traveling down the interstate at 20 m/s. He sees a speeder traveling at 50 m/s approaching from behind. At the moment the speeder passes the trooper, the trooper hits the gas and gives chase at a constant acceleration of 2.5

Assuming that the Speeder continues at 50 m/s, how long will it take the trooper to catch up to the speeder?

24 seconds

Explanation:

The speeder moves at constant velocity, so we can write the position of the speed at time t as:

where

is the velocity of the Speeder

t is the time in seconds

Here is measured relative the the position at which the Speeder overcomes the trooper

The position of the trooper instead is given by

where:

is the initial velocity of the trooper

is its acceleration

The trooper reaches the speeder when their positions are the same:

Substituting the values, we get:

which has two solutions:

t = 0 (initial instant)

So, the trooper reaches the Speeder after 24 seconds.

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