An object on point $A$ with the initial velocity of $\dot{\bf{x}} (t)$ have a maximal acceleration of $a$. What is the fastest path for the object to get to point $B$?
I thought this should be all over the Internet but I don't know what to search for. So, thanks for any help!
Following is the equation you need: s = $\dot{\bf{x}} (t) \times t + \frac{1}{2} a \times t^2$, where s is the distance from A to B. If s is given you could calculate t.