Solve the each part of given question:
Question: A police car at rest is passed by a zooming speeder traveling at 100 miles per hour (mph). The police car catches up to the speeder in 500 meters (m), maintaining a constant acceleration. Answer the following questions in SI units.
Part I: How long did it take for the police car to overtake the speeder?
Part II: What was the required acceleration for the police car?
Part III: What was the speed of the police car at the overtaking point?
Please use as much detail as required in your answer. Thanks.