Aspeeder passes a parked police car at a constant speed of 23.3 m/s. at that instant, the police car starts from rest with a uniform acceleration of 2.75 m/s 2 . how much time passes before the speeder is overtaken by the police car? answer in units of s.

32s

Explanation:

We must establish that by the time the police car catches up to the speeder, both have travelled a certain distance during the same amount of time. However, the police car experiences accelerated motion whereas the speeder travels at a constant velocity. Therefore we will establish two formulas for distance starting with the speeder's distance:

and the police car distance:

Since they both travel the same distance x, we can equal both formulas and solve for t:

Two solutions exist to the equation; the first one being

The second solution will be:

This result allows us to confirm that the police car will take 32s to catch up to the speeder