I want to intercept two objects, making both their time and velocity the same. One has acceleration to achieve this goal, while the other is moving at a constant rate. Furthermore, I want them to intersect at a specific intersection point.
The easiest permutation of this is a 1 dimensional line with the faster, unpowered object reaching the intersect point first. The powered object has to accelerate at a specific time to finish acceleration at the intersect point matching velocity at the intercept. I am pretty sure it has to be a system of equations, but I'm having a lot of trouble trying to figure out how to set it up.
I know that obj1: x2 = x1 +v1*t +.5at^2 and obj2: x2 = vt + x1
The x2 values should be equal so: x1 + v1t + .5at^2 = vt + x1
but I'm not quite sure what to do next because the vs and xs are specific to their objects.
Edit: I thought about this some more and a simpler version would be an accelerating object reaching a specified position with a specified velocity at a specified time, since the target will always reach the point at the same time. Still working this out, but maybe I'm a bit closer.