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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!

arax
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    Is the object subject to a force $F=ma$ (for $m$ the mass of the object)? If so, see https://en.wikipedia.org/wiki/Brachistochrone_curve. – Plutoro Aug 17 '15 at 02:38
  • @AlexS Nope, the direction of its acceleration is arbitrary – arax Aug 17 '15 at 02:49

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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.

Moti
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