I'm trying to do the following problem: A car can accelerate and brake with constant acceleration, both with the magnitude (a). The car has a maximum velocity (v). The car needs to cover the distance (L), starting and ending at rest. a) How long will it take the car to cover the distance if the maximum velocity (v) is NOT reached? b) How long will it take the car to cover the distance if the maximum velocity (v) IS reached? I only become increasingly confused the more I try to understand this question. If the car does not reach its maximum velocity in the first question, then how will it do so in the second when the acceleration and distance is a constant? If I ignore (v), then i get this: S=0.5at^2 (L/2)=0.5at^2 t=sqrt(aL) Can anyone help?