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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.