My background is in computer graphics programming, so please forgive me if any terminology or notation seems off.

This problem would take place in two dimensional space. There are two objects each with known positions (x,y). Each object has a known initial velocity (Vx, Vy). Each object can accelerate at a known rate, but cannot accelerate faster or slower than its given rate, unless its acceleration is 0. Each object can accelerate in any direction, but each object has a known speed limit that it cannot accelerate past.

If we are given the direction of acceleration for one object, assuming that each object will simply coast in a straight line once its speed limit is reached, how do we determine what direction the second object must accelerate in order to collide with the first object (assuming each only occupies a single point given by their position).

Any suggested resources or references to read up on to better understand the problem are greatly appreciated.