This is a differential equation problem.

Problem 3: On a straight stretch of road of length L there were two stop signs at the two ends. Assume you follow traffic laws and stop at these signs. Your car can accelerate at a constant a1 and decelerate at another constant a2). Compute the shortest time to travel from one stop sign to another if there is no speed limit in between. Do it again if the speed limit between the signs is vM