---
title: "A particle of mass \\(m\\) is constrained to move along the positive \\(x\\)-axis under the influence of a conservative force associated with the potential energy function \\(U(x) = \\dfrac{a}{x^2} – \\dfrac{b}{x}\\), where \\(a\\) and \\(b\\) are positive constants.  The particle is released from rest at \\(x = \\dfrac{a}{b}\\).  In terms of \\(m\\), \\(a\\), and \\(b\\), what is the maximum speed achieved by the particle during its subsequent motion?"
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url: "https://nerd-notes.com/ubq/120685/"
date_modified: "2026-08-23T04:42:40+00:00"
---

# A particle of mass \(m\) is constrained to move along the positive \(x\)-axis under the influence of a conservative force associated with the potential energy function \(U(x) = \dfrac{a}{x^2} – \dfrac{b}{x}\), where \(a\) and \(b\) are positive constants.

The particle is released from rest at \(x = \dfrac{a}{b}\).

In terms of \(m\), \(a\), and \(b\), what is the maximum speed achieved by the particle during its subsequent motion?

A particle of mass \(m\) is constrained to move along the positive \(x\)-axis under the influence of a conservative force associated with the potential energy function \(U(x) = \dfrac{a}{x^2} - \dfrac{b}{x}\), where \(a\) and \(b\) are positive constants.

The particle is released from rest at \(x = \dfrac{a}{b}\).

In terms of \(m\), \(a\), and \(b\), what is the maximum speed achieved by the particle during its subsequent motion?

- **A.** \(\dfrac{b}{2\sqrt{2ma}}\)
- **B.** \(\dfrac{b}{2\sqrt{ma}}\)
- **C.** \(\dfrac{b}{\sqrt{2ma}}\)
- **D.** \(\dfrac{b}{\sqrt{ma}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120685/*