you have the acceleration as a function in time , you must integral the acceleration over time to get the speed because
a = du/dt , and then integral the speed over the time to get the distance as function in time , put the distance equal to 200 in the function to get the time then put the result in the function of the speed .
you can get the constants of of each integral from the initial conditions where s=0 then d=0,and u = 0
if you cant do this alone , i will help you another time