Question

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 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 = -0.360 m/s² for a time interval Δt₂. Find the minimum time interval of travel Δt and the time interval Δt₁.
Hint: It is much easier to do this problem graphically. First draw an acceleration versus time graph. What does the area under this graph physically mean? You should be able to get a relation between Δt₁ and Δt₂. Then draw a velocity versus time graph. What does the area under this graph physically mean? You should be able to get another relation between the two time intervals. Now you have two equations and two unknowns.