Question

A commuter train travels between two downtown stations. Because the stations are only 1.36 km apart, the train never reaches its maximum possible cruising speed. During rush hour the engineer minimizes the travel time t between the two stations by accelerating at a1 = 0.100 m/s2 for a time t1 and then immediately braking with acceleration a2 = -0.410 m/s2 for a time t2. Find the minimum time of travel t and the time t1.