This problem is limited to 2 dimensions (XY plane) + time.
There are two objects, A and B.
Both objects move in a straight line. Object A has an initial speed and decelerates (constant deceleration). Object B's speed is constant.
Initially, A is at InitialPointA. It has an initial speed InitialSpeedA. It's moving in direction DirectionA. It decelerates at DecelerationA.
Initially, object B is at InitialPointB. It moves at a constant speed of SpeedB.
Need to find the direction object B must travel in order to intercept (hit) object A at the earliest point in time.
Per "amd"'s suggestion, I'm editing/adding the approach I've taken so far: (Note: DirectionA is a unit vector)
CurrentPointA(t) = ((InitialSpeedA * t - ((DecelerationA * t^2) / 2)) * DirectionA) + InitialPointA
The distance B must travel to intercept A at the current time t is
InterceptDistanceB = length(InitialPointB - CurrentPointA(t))
The distance B travels during time t is simply SpeedB * t
What must be found is the time t where
InterceptDistanceB = SpeedB * t
i.e.,
length(InitialPointB - CurrentPointA(t)) = SpeedB * t