- #1

OmniNewton

- 105

- 5

## Homework Statement

Two trains start from rest from two stations 5.0 km apart and travel, on two parallel railroad tracks, in opposite directions. One train accelerates uniformly at 2.5 m/s^2 and the other has a constant acceleration of 4.0 m/s^2.

How far from the first station will they meet?

## Homework Equations

1. d= at^2

2. v^2 = u^2+ 2ad

3. t= v-u/ a

## The Attempt at a Solution

__Train 1 relative to Train 2__

Initial velocity = 0 m/s

Acceleration = 6.5 m/s^2

Displacement = 5000m

v^2 = u^2+ 2ad

v = Square root of u^2 + 2ad

v= Square root of 2ad

v= Square root of 2(6.5 m/s^2) (5000m)

v= Square root of 65000 m^2/s^2

v= + or - 255 m/s

t= v-u/ a

t= 255ms^-1/6.5m/s^-2

t= 39 seconds

__Train 1__

d= at^2 because initial velocity = 0

d= (2.5 ms^-1) (39 seconds)

d= 97.5m

Therefore they will meet 97.5m from the first station.

However this answer does not make sense to me because if I solve for distance with the other train it does not add to 5000m or 5.0 km. I do not know what I did wrong.

Thanks In Advanced