Question

An unmarked police car traveling a constant 80.0 km/h is passed by a speeder traveling 115 km/h . Precisely 1.50 s after the speeder passes, the police officer steps on the accelerator; if the police car's acceleration is 2.50 m/s2 , how much time passes before the police car overtakes the speeder after the speeder passes (assumed moving at constant speed)?

Answer 1

Let the speed of the speeder

The speeder moves with constant velocity.

∴acceleration of the speeder

Let the initial speed of the police vehicle

Acceleration of the police vehicle

Let the relative velocity of the police vehicle with respect to the speeder be

Relative velocity of the speeder with respect to the police vehicle

Let the relative acceleration of the police vehicle with respect to the speeder be

∴

The police vehicle starts acceleration 1.5 secs after the speeder passes them.

So, the distance between the police vehicle and speeder after 1.5 sec

∴d

Let the time taken by the police vehicle to overtake the speeder be t secs after it begins acceleration.

∴

∴

Total time taken to overtake the speeder