Physics: Train Problem?

Question

I don't understand this...PLEASE PLEASE HELP!!! thanks

A train travels between stations 1 and 2. The engineer of the train is instructed to start from rest at station 1 and accelerate uniformly between points A and B, then coast with a uniform velocity between points B and C, and finally accelerate uniformly between points C and D until the train stops at station 2. The distances AB, BC, and CD are all equal, and it takes 5.00 min to travel between the two stations. Assume that the uniform accelerations have the same magnitude, even when they are opposite in direction.
a) How much of this 5.00 min period does the train spend between points A and B?
b) How much of this 5.00 min period does the train spend between points B and C?

Answer 1

Interesting problem; you don't have the distance.
Lets let V(max) be the maximum velocity achieved.
And let the total distance be S.
Then the average velocity for leg one:
V(avg1) = [v(zero) + v(final)]/2 = V(max)/2
Average velocity for leg three:
V(avg3) = [v(zero) + v(final)]/2 = V(max)/2

Time:
Leg1(Leg3):
t = D/v
t = (S/3)/(V(max)/2)
t = 2S/3V(max)
Leg2:
t = D/v
t = (S/3)/V(max)
t = S/(3V(max))

Ratio of time spent:
A -----> B : B ----->C : C ----->D
2 : 1 : 2
Hence Time A -----> B = (2/5)(5min) = 2min
Time B -----> C = (1/5)(5min) = 1min