Deceleration necessary to prevent a train collision

[rezal]

Homework Statement

The engineer of a passenger train traveling at vP sights a freight train whose caboose is distance D ahead on the same track. The freight train is traveling at vF in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant deceleration of a, while the freight train continues with constant speed.
For what range of decelerations a will the train collision be avoided?
Givens: vP,vF,D,

Homework Equations

Passenger Train: D=vP-.5at^2
Freight Train: x(t)=vFt
vP=vF+at

The Attempt at a Solution

I [/B]planned on solving this by substituting
t=(vP-vF)/a
into the equation for the passenger train
D= vP((vP-vF)/a) - .5a((vP-vF)/a)^2
and then solving for a but I was told that this is incorrect?

 

[SammyS]

Homework Statement

The engineer of a passenger train traveling at vP sights a freight train whose caboose is distance D ahead on the same track. The freight train is traveling at vF in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant deceleration of a, while the freight train continues with constant speed.
For what range of decelerations a will the train collision be avoided?
Givens: vP,vF,D,

Homework Equations

Passenger Train: D=vP-.5at^2
Freight Train: x(t)=vFt
vP=vF+at

The Attempt at a Solution

I [/B]planned on solving this by substituting
t=(vP-vF)/a
into the equation for the passenger train
D= vP((vP-vF)/a) - .5a((vP-vF)/a)^2
and then solving for a but I was told that this is incorrect?

It is incorrect, but who told you that, and did they give you a reason?

 

[rezal]

My TA did but he didn't really give any particular reason as to why.