Constant Acceleration?

Question

(a) If the maximum acceleration that is tolerable for passengers in a subway train is 1.74 m/s2 and subway stations are located 836 m apart, what is the maximum speed a subway train can attain between stations? (b) What is the travel time between stations? (c) If a subway train stops for 24.0 s at each station, what is the maximum average speed of the train, from one start-up to the next?

Answer 1

Calculate the speed when accelerating to the midpoint (it will then decelerate to 0 over the same distance since the accel limit must apply to braking):
s = 836/2
(a) s = v^2/(2a); v = sqrt(2as)
(b) t = v/a; total time = 2t
(c) v(ave) = 2s/(2t+24)