Question

There is a 1500 mile race course. I MUST have a top speed of 36 meters/s (meaning I cannot go over 36). The max foward acceleration is 4 m/s squared and the max backward acceleration is 6 m/s squared.
I start at 600m and must go to the 800m mark (I must travel 200m). What is an equation for the fastest time that I could get to 800m? What is the position, time and velocity of my vehical?