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 Possible solution by Jer)

I believe Jer's solution is correct, "T = 2D/V"

I think we can rule out using special relativity, since 1/(1-v^2/c^2)^.5 only comes into play as velocity approaches the speed of light, and we are looking to maximize the time.   So unless we're talking about the particle travelling the opposite direction and going all the way to the end of the universe and back to itself (less the distance D), then I believe we are safely in the realm of Newtonian physics.

Furthermore, the acceleration "can't increase".  OK, suppose it could decrease.   In that case, the faster acceleration earlier in the trip would get the particle to point B in less time than would be predicted just by looking at the final velocity, and assuming constant acceleration.

So, I agree with Jer.

Posted by Larry on 2004-05-06 17:16:17