A particle is travelling from point A to point B. These two points are separated by distance D. Assume that the initial velocity of the particle is zero.

Given that the particle never increases its acceleration along its journey, and that the particle arrives at point B with speed V, what is the longest time that the particle can take to arrive at B?

(In reply to

Solution by Brian Smith)

I wish you (or someone else) had brought this up in the queue, as I
would have specified the two possibilities and asked for the two
answers.

You've got a point, of course.... But this is due to the
phrase "never increases its acceleration", which Brian is taking to
mean *magnitude* of the acceleration (which is a vector).
Clearly, in this interpretation of this problem, the direction of the
acceleration is changing.

Let me add to the problem "**How does your answer change if the direction of motion is exclusively along a straight line between A and B?**" (Would a scholar please add this line to the problem?)

Thanks,

-SK