A commuter train travels between two downtown stations. Because the stations are only 1.00 km apart, the train never reaches its maximum possible cruising speed. During rush hour the engineer minimizes the time interval ∆t between two stations by accelerating for a time interval ∆t1 at a rate a1 = 0.100 m/s2 and then immediately braking with acceleration a 2 = -0.500 m/s2 for a time interval ∆t 2 Find the minimum time interval of travel ∆t and the time interval ∆t1.