Constant Acc with two particles

[pappaloo]

Im having a problem with this question, which is probably rather simple but I am making a lot harder than it needs to be.

A high-speed train is traveling at 44.72m/s and it sees a sidecar a distance of 676m ahead. The sidecar is traveling with a constant velocity or 8.056m/s.

The question asks what the magnitude of the resulting constant deceleration must be if a collision is to be just avoided.

I took two of the derived C.A. equations and in each one had two unknowns which were x(final) and t.

I then equated the two equations and solved the linear system for t at which I arrived with an answer of 47.26s

From there it is quite easy to figure out the rest of the question, but I am not sure if I am doing this question the best way or even correctly for that matter.

Any suggestions or comments would be greatly appreciated

[Doc Al]

I'm not sure exactly what you did, but here are two ways to approach it:
(1) Write the postions of each (sidecar and train) as a function of time. Set them equal, and solve for t. (This is what you tried, I believe.) Of course, the acceleration is a variable. Since the equation is a quadratic, you can find a constraint that will tell you the minimum acceleration that just avoids the collision.
(2) Look at the motion from the frame of the sidecar and solve it directly with a kinematic equation.

And welcome to PF!