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Question

If the maximum acceleration that is tolerable for passengers in a subway train is 1.34 m/s2 and subway stations are located 880 m apart. What is the maximum speed, a subway train can attain between stations?


A

38 m/s

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B

68.6 m/s

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C

34.3 m/s

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D

51.2 m/s

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Solution

The correct option is C

34.3 m/s


The acceleration time curve for the given situation will be

Now write equation

a = 1.34 m/s2

The distance between 2 railway stops is 880 m.

So, the train travels with acceleration 1.34 m/s2 fot the half journey i.e.440 m

If the total time taken for the journey is T then the train is accelerated for T/2 sec

a = dvdt = 1.34

v0dv=t01.34dt

v = 1.34 t ....... (1)

for the time T2 displacement is 440 m

Now v = dsdt = 1.34t

= 4400ds=T20 1.34t dt

440 = 1.34 t22]T20

T = 51.25 sec.

Now substitute (T2) in equation (1)

V = 1.34 × (51.252)

V = 34.335 m/s


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