I want to model a particle with an arbitrary initial velocity, and estimate the time it takes to reach a final point given a constant magnitude of acceleration. It should take the quickest path to the point. This takes place on a 2D plane.
I can't figure out how to model the acceleration for the particle, since when I think about the problem it seems like the acceleration direction should change as the particle's position relative to the final point changes. I don't know how it would change, or even why. Part of me thinks that the acceleration should be in a constant direction, but I can't figure out which direction that would be either.
As you can see, I am fairly lost here. Is there a general equation for the ideal direction of acceleration here? Thanks for any help you can provide. If it is at all relevant, this is for a simulation I'm writing in Python to predict the time it takes a particle with some initial velocity vector to reach a given point.