When a high speed passenger train travelling at 161 km/h rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance D = 676m ahead. The locomotive is moving at 29.0km/h.

What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided?

This is what I ended with so far

x[locomotive] = 676 + 8.0555t [8.0555 ms^-1 = 29.0kmh^-1]
v[final] = 0
v[initial] = 44.7222 ms^-1 [44.7222ms^-1 = 161kmh^-1]
a = ?

So solving for a, I end up with an equation:
a = -44.7222/[(2)(676+8.055t)]

so how do I approach at finishing this question...

Question. Is the locomotive headed towards the passenger train, or are they going the same direction?

Going in the same direction.