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

Is it in the wording? by mike)

The problem says the initial velocity is zero. It doesn't say the
initial acceleration is zero. And since it clearly moves, I think
one can safely say that the initial acceleration is non-zero.