A car braked with constant deceleration of 16 ft/sec^2 takes 200 ft to come to a complete stop. How fast was the car traveling when the breaks were first applied?

Question

A) if the brakes were first applied when t = 0 at position s(0) = 0, the initial velocity is an unknown, say V. Solve the differential equation s"(t) = -16 with initial conditions s(0) = 0 and v(0) = V.

B) since the velocity decreases 16 ft/sec^2 every second, it will take t = V/16 seconds for the car to stop. Since it stops after 200 feet, solve s(t) = 200 where t = V/16 for the unknown initial velocity V.