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Here's the problem I'm solving:

A particle of mass $m$ can only move along the $x$-axis and is subject to an interaction described by the potential energy function $U\left(x\right) = -Ax^4$, where $A > 0$ is a constant. The particle's energy is $E = 0$ and its position at $t = 0$ is $x_0 > 0$.

Assume that $v_0 < 0$ and estimate (analytically) how long it would take for this particle to approach $x = 0$.

I solved the equation of motion and got $$t = \sqrt{\frac{m}{2A}}\left(\frac{1}{x} - \frac{1}{x_0}\right).$$

The time it takes for the particle to reach $x = 0$ is $t = \infty$, but it's clear to me that this isn't what's being asked for. I don't know how to approach this problem and I'd like some guidance.

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closed as off-topic by ZeroTheHero, Jon Custer, G. Smith, StephenG, John Rennie Jan 24 at 6:58

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You're probably not supposed to actually solve it, just estimate it using some simple approximations. For example, you could figure out the initial velocity $v$ and then take $x_0/v$ as a rough timescale.

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