A express train travels along a straight line between two stations, A and D. Stations B and C are spaced evenly along the line between A and D. The engineer leaves A and accelerates at a constant rate until he passes station B, at which time he coasts with constant velocity. When he reaches station C, he slows down at the same rate he used for the first segment of the trip, thereby coming gently to rest at station D. Given that the total trip requires 5 mins, how much time is spent going from

Question

A express train travels along a straight line between two stations, A and D. Stations B and C are spaced evenly along the line between A and D. The engineer leaves A and accelerates at a constant rate until he passes station B, at which time he coasts with constant velocity. When he reaches station C, he slows down at the same rate he used for the first segment of the trip, thereby coming gently to rest at station D. Given that the total trip requires 5 mins, how much time is spent going from 
1) A to B?
2) B to C?
3) C to D?
 Please help me ASAP!!

Steve · Answer

Let's say that the three times to traverse AB,BC,CD are x,y,z respectively. They add to 5 min.

The time to accelerate is the same as the time to decelerate, so x=z.

If the acceleration is a m/s^2, we have

x+y+z = 5
1/2 ax^2 = axy
1/2 ax^2 = axz - 1/2 az^2

We can factor out the a from all the terms, and we are left with

2x+y = 5
x=2y

Now solve for x and y

Anonymous · Answer

Which physics equations should I use?