1. The problem statement, all variables and given/known data a A sportscar can accelerate uniformly to 120 mi/h in 30s. Its maximum braking rate cannot exceed 0.7g. what is the minimum time required to go 1/2 mi, assuming it begins and ends at rest? 2. Relevant equations I drew a graph of v(t) vs t. where the initial acc. goes up to a certain time, t1, then decelerate to a rest at t2. 3. The attempt at a solution acc= 4 mi/min V1 = 4t For convenience i drew another graph for when the car dec. Therefore: acc= -0.7g V2 = 4t1 - 0.7gt Integrate: d = 0.5 = int ( 4t, t, 0, t1) + int (4t1 - 0.7gt, t, 0, t2) => 2t1^2 + 4t1t2 - 0.7g/2 t2^2 Here is where i got lost. i know that t = t1 + t2 but i dont know how to derive t with its components to get the minimum time. please help and thank you.