Train collision (linear kinematics)

[walking]

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.

 

[Doc Al]

Also, the minimum deceleration would be if the passenger train stops exactly when they meet.

Why would the passenger train have to stop at that point?

 

[walking]

Why would the passenger train have to stop at that point?

I thought it would give the slowest rate of deceleration if it comes to a stop at the maximum displacement to avoid collision, ie right when they meet. Maybe my intuition is wrong?

 

[Doc Al]

I thought it would give the slowest rate of deceleration if it comes to a stop at the maximum displacement to avoid collision, ie right when they meet. Maybe my intuition is wrong?

Yes, your intuition is wrong. What you want to ensure is that when they meet the passenger train doesn't overtake the freight train (and thus collide). But to do that, it doesn't have to stop dead. Hint: The freight train is moving.

 

[Orodruin]

Another suggestion: Do everything in the rest frame of the freight train instead.

 

[neilparker62]

Another suggestion: Do everything in the rest frame of the freight train instead.

In which case the OP's intuition would indeed be correct - final velocity of train relative to freight train would be zero!

 

[Orodruin]

In which case the OP's intuition would indeed be correct - final velocity of train relative to freight train would be zero!

Indeed.