Collision Avoidance - Constant Deceleration

[Beamsbox]

Alright, once again I've failed myself and now I think I've wasted way too much time on trying to figure this out. I just want a bit of help in setting this thing up and perhaps a short description of which variables I need to find first. Any help, much appreciated of course. Thanks all.

Homework Statement

Basically you have two trains, the first traveling at 161km/hr and the second traveling at 29km/hr and 676m ahead of the first. The first slams on his brakes. What magnitude of deceleration must result if a collision is to be just avoided?

Homework Equations

Given equations, not sure which I need to use first, etc.
v=v₀ + at
x-x₀ = v₀(t)+(1/2)at²
v² = v₀² + 2a(x-x₀₎
x-x₀ = (1/2)(v₀+v)t
x-x₀ = vt-(1/2)at²

The Attempt at a Solution

So, the various attempts I've made seem to lead me to nowhere. The thing that throws me off the most, is I know that if I find the deceleration across the 676m distance, it won't work because the second train has obviously moved.

I'm thinking that I need to somehow find the amount of time the second train takes to travel the distance that it moves while the deceleration takes place, and then use that to determine the distance it travels. From there I could easily calculate the deceleration over the entire distance. BUT! I don't know how to find that time, and I'm thinking that once you write the CORRECT equations, and substitute them into each other perhaps that time will cancel out... leaving you with all the information you need.

But, like I said, I'm lost. And haven't a clue on where to start. I keep confusing myself from all sorts of different angles.

Thanks again for any help!

 

[kuruman]

Look at it from the point of view of the leading train. You are at rest and you see a train coming at you with the (relative) velocity of 161 - 29 = 132 km/hr. The distance between you and the train is 676 m. What deceleration does the train need to have to stop over that distance? Use the third kinematic equation that you posted to find out.

 

[Beamsbox]

Finally got the answer I was supposed to get. I had correctly set up the problem (multiple times), but I had apparently converted between km/hr and m/s incorrectly. I stuck with what you were telling me and after a bit I realized my mistake.

Thank you for your time and input, Kuruman.