---
title: "A particle moves in one dimension along the positive \\(x\\)-axis. Starting at position \\(x = 0\\) with an initial speed \\(v_0\\) in the \\(+x\\)-direction, the particle experiences an acceleration given by \\(a(x) = -\\beta x^2\\), where \\(\\beta\\) is a positive constant. Which of the following expressions represents the distance \\(D\\) the particle travels before momentarily coming to rest?"
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url: "https://nerd-notes.com/ubq/120478/"
date_modified: "2026-08-23T04:39:03+00:00"
---

# A particle moves in one dimension along the positive \(x\)-axis. Starting at position \(x = 0\) with an initial speed \(v_0\) in the \(+x\)-direction, the particle experiences an acceleration given by \(a(x) = -\beta x^2\), where \(\beta\) is a positive constant. Which of the following expressions represents the distance \(D\) the particle travels before momentarily coming to rest?

A particle moves in one dimension along the positive \(x\)-axis. Starting at position \(x = 0\) with an initial speed \(v_0\) in the \(+x\)-direction, the particle experiences an acceleration given by \(a(x) = -\beta x^2\), where \(\beta\) is a positive constant. Which of the following expressions represents the distance \(D\) the particle travels before momentarily coming to rest?

- **A.** \(\left( \dfrac{v_0^2}{2\beta} \right)^{1/3}\)
- **B.** \(\left( \dfrac{3v_0^2}{2\beta} \right)^{1/3}\)
- **C.** \(\left( \dfrac{3v_0^2}{\beta} \right)^{1/3}\)
- **D.** \(\left( \dfrac{6v_0^2}{\beta} \right)^{1/3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120478/*