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walking

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## Homework Statement

A passenger train is traveling at 29ms^-1 and a freight train is traveling 360m ahead of it at 6ms^-1 in the same direction on the same track. The driver of the passenger train has a reaction time of 0.4s before he starts decelerating. What is the minimum deceleration to avoid colliding with the freight train?

## Homework Equations

x-0=29t+0.5at^2

0=29+at

x-350.8=6t

## The Attempt at a Solution

I tried solving this as follows but my answer is wrong according to a solution I found online. Where am I going wrong?

First I calculated that when the driver starts decelerating, the separation of the trains will be 350.8m. I then let the initial time be this point in time (ie when they are 350.8 apart) and I let x=0 at t=0. So initially, the passenger train is at x=0 and the freight train is at x=350.8. I let the time they meet be t and the displacement of both trains be x at this time. Also, the minimum deceleration would be if the passenger train stops exactly when they meet.

Based on this, I got the following equations:

For the passenger train we get two equations:

x-0=29t+0.5at^2

0=29+at (since it comes to a stop when they meet)

For the freight train:

x-350.8=6t

Solving these, I got a=-0.703, however the solution I found online (in a pdf document of solutions to the problems in Tipler/Mosca 5th edition; this problem is chapter 2 q96) gives -0.754.