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?
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