Suppose you have a car with a maximum acceleration of a = 6.0 m/s² and a maximum deceleration from braking of a = -8.0 m/s². We want to find the minimum time it would take you to start from rest, cover 500 m, and come to a stop at the 500 m mark. You do this by accelerating as much as possible for a part of the 500 m, followed by a period of maximum deceleration to the final stop. Find the minimum time.
