1. The problem statement, all variables and given/known data Bob and Villie are able to tolerate acceleration of 0.2g, the driver wants to accelerate from 250km/h to 300 km/h on a curved piece of track, the radius of curvature is 5km, what is the minimum time the driver can use to change speed? 2. Relevant equations total acceleration = tangential acceleration + radial acceleration speed = initial speed + tangential acceleration x time 3. The attempt at a solution given that total acceleration must not exceed 0.2g, radial acceleration increases as tangential acceleration decreases. So what i did was integrate tangential acceleration over a time period from x to y which should equal to the change in speed. Integration (x to y) tangential acceleration dt = 13.89 m/s i was hoping to eventually end up with an equation that goes m(x-y) = 13.89 and then solve for x-y but when i plug in the above equations in b for tangential acceleration, I get this extremely complicated and unsolvable quadratic formula if i attempt to express the equations in terms of t. Anyone?