A subway car, travelling from one station to another, undergoes three distinct p

Question

A subway car, travelling from one station to another, undergoes three distinct periods of motion: it first accelerates, then it travels with constant velocity, and then it decelerates. Consider the case when it is travelling between two stations which are   1070 m    apart. During the first stage, it starts from rest and accelerates at a rate of   1.31 m/s2    for   4.5 s   . After this, it travels with constant velocity until it is   160 m    from the second station. Finally, it decelerates at a constant rate.

Part A-How far does the subway car travel during the initial stage, during which time it is accelerating?

Part B-How long does the train move at constant velocity?

Part C-What is the acceleration of the train during the third stage?

Part D-What is the total amount of time it took for the subway to travel between the two stops?

Explanation / Answer

Total distance = 1070 m

first stage

starts from rest and accelerates at a rate of   1.31 m/s2    for   4.5 s

SEcond stage

it travels with constant velocity until it is   160 m    from the second station

Third syage

it decelerates at a constant rate.

Part A

S = 1/2 at2 = 0.5*1.31*4.52 = 13.26 m

Part B

Distance = 1070 - 120 - 13.26 = 936.74 m

Time = 936.74 / V where V =constant velocity

Part C

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