Mechanics question

I'm attempting to understand an issue that a mechanics student is having, and I was wondering if someone could break down this particle mechanics equation for me so I know where it fits in:

V(x)=-A|x|^(n)

The exact problem that they are dealing with is:

A particle moves towards [x = 0] under the influence of a potential V( x ) = -A|x|^(n) (assume n > 0). The particle has barely enough energy to reach x = 0. For what values of n will it reach x = 0 in a finite time?

Precisely, I need to know what values A, x, and n are supposed to represent. I'm not specifically a mechanics student, but these sort of things always spark my interest in a self-teaching direction.

 

You are correct. I understand the basic mathematical principles, but since I'm not familiar with these types of physics, I was not sure if the A and n were arbitrary (I had assumed x is a variable in this case, and representative of some aspect of the particle, but was not clear on which), or if they were a significant constant. V(x), as I would understand it, is simply the calculated potential of the particle in x position.

[tex]KE = \frac {1}{2}m (\frac {dx}{dt})^2 [/tex]

I'll work with it a bit, and see what I can come up with. Thanks for the starting point! :)