All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > General
Particle Acceleration (Posted on 2004-05-06) Difficulty: 2 of 5
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?

No Solution Yet Submitted by SilverKnight    
Rating: 2.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution My uninfluenced solution | Comment 13 of 24 |

I assume that decreasing the acceleration will not maximize the time, that the puzzle is one-dimensional, and both D and V are positive.

Considering the movement of the particle on an x-y graph, it should look like a parabola.  The equation of the parabola is y=Ax/2, where y=distance, A=acceleration, and x=time.  The speed is equal to Ax.  When this parabola intersects y=D, the particle hits point B.

Before maximizing time, I'm just going to figure out the possibilities for A.

The coordinates of the intersection of y=Ax/2 and y=D:

The speed of this intersection will be A*sqrt(2D/A).

It seems that there is only one possibility for A, so the time is already maximized.

Now, to prove my first assumption: "that decreasing the acceleration will not maximize the time."  Decreasing the acceleration will make the ending speed slower then it would have been.  Since it must be at speed V, the beginning speed must be faster to compensate.  This makes the time shorter.

  Posted by Tristan on 2004-05-07 23:16:25
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information