Deceleration of Train to Avoid Collision

[egrr10]

Homework Statement

The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 m/s^2, while the freight train continues with constant speed. Take x=0 at the location of the front of the passenger train when the engineer applies the brakes. Find the deceleration of the passenger needed in order to avoid collision.

Homework Equations

Vx^2=Vox^2 + 2ax(x-xo)

The Attempt at a Solution

I'm using V of the freight train as the final and the V of the passenger as the initial and 200m as the distance.
Rearranging the equation,
(15^2-25^2)/(200*2)=-1m/s^2

Or do I use the relative velocity between passenger train and freight train 10m/s (25-15) as the initial and 0m/s (coming to a complete stop) as the final.
(0^2-10^2)/(200*2)=-0.25m/s^2

 

[mfb]

The first one cannot be true as the passenger train has more than 200m to slow down. It is possible to fix it, but using the second approach is much easier.