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 the exact time.
by Ady TZIDON)
2*D/V is the longest time (which is what the puzzle asks for), so it is the solution. Note that the problem specifies that there is no increase in acceleration, but there can be a decrease in acceleration.
2*D/V corresponds to the case where there is constant acceleration (no decrease), like when you drop an object that is subject to gravity in a frictionless environment, such as the Moon or a vacuum tube. The time is shorter than 2*D/V if there is a decrease in acceleration, like when you drop an object on Earth and friction acts to reduce the velocity.