What is the maximum speed?

Question

If the maximum acceleration that is tolerable for passengers in a subway train is 1.31 m/s^2, and subway stations are located 626 m apart, what is the maximum speed a subway train can attain between stations?

Answer 1

I already answered this!

Assuming that that acceleration maximum is in either direction, ie, for braking as well as accelerating.

The train has to spend half the time and distance accelerating at 1.31 m/s2, and the second half deccelerating at the same rate.

d = ½at²

313 = ½(1.31)t²

t² = 478

t = 22 seconds. total travel time is 44 seconds.

2) total distance = 626 m

total time = 44+15 = 59s

Av V = 626/59 = 10.6 m/s

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Answer 2

626=1/2(1.31)T ^2,T^2=955.725, T=30.9148seconds

V=1.31T,V=30.9148x1.31=40.5m/sec.

Answer 3

74.5 mph

Answer 4

Assume that acceleration up to top speed then equal acceleration in the negative.  So the distance is now cut in half. or 313 meters to max velocity.  Let v=velocity, x=distance, and t=time.  we use two principle equations

v=x/t

time=x/v

and the other equation

a= 1/2 at^2

substitute for time and you get

time=(2x/a)^-2=x/v

Solve for velocity.

v= x/((2x/a)^-2)

v=14.31meters per second or 51516 meters per hour.

this is about 82.43 miles per hour.