A local train leaves station A; it gains speed at the rate of 1 ms ^−2 for first 6 s and then at the rate of 1.5 ms ^ −2 until it has reached the speed of 12 m/s. The train maintains the same speed until it approaches station B; brakes are then applied, giving the train a constant deceleration and bringing it to a stop in 6 s. If the total running time of the train is 40 s. Find (a) the distance between stations A and B. (b) Draw acceleration-time, velocity-time, and the position-time relation of motion.