Question: A particle moves toward x = 0 under the influence of a potential V (x) = A|x|n, where A > 0 and n > 0.

A particle moves toward x = 0 under the influence of a potential V (x) = −A|x|n, where A > 0 and 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?

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