### Find out the minimum time interval of travel

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Q. A commuter train travels between two downtown stations. Since the stations are only 1.38 km apart, the train never reaches its maximum possible cruising speed. Throughout rush hour the engineer minimizes the travel interval Δt between the two stations by accelerating for a time interval Δt1 at a1 = 0.100 m/s2 and then immediately braking with acceleration a2 = -0.440 m/s2 for a time interval Δt2. Find out the minimum time interval of travel Δt and the time interval Δt1.

A hotel elevator ascends 140 m with a maximum speed of 5.80 m/s. Its acceleration and deceleration both have a magnitude of 1.50 m/s2.

(a) How far does the elevator move even as accelerating to full speed from rest? (m)

(b) How long does it take to make complete trip from bottom to top? (s)

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