---
title: "A proton of mass \\(m\\) and charge \\(+e\\) is constrained to move along the \\(x\\)-axis in a region where the electric potential \\(V(x)\\) is shown in the graph. At position \\(x = 1.0\\text{ m}\\), the proton has a kinetic energy of \\(2.0e V_0\\) and is traveling in the \\(+x\\)-direction. What is the maximum speed achieved by the proton during its subsequent motion?"
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url: "https://nerd-notes.com/ubq/124622/"
date_modified: "2026-09-28T14:08:52+00:00"
---

# A proton of mass \(m\) and charge \(+e\) is constrained to move along the \(x\)-axis in a region where the electric potential \(V(x)\) is shown in the graph. At position \(x = 1.0\text{ m}\), the proton has a kinetic energy of \(2.0e V_0\) and is traveling in the \(+x\)-direction. What is the maximum speed achieved by the proton during its subsequent motion?

A proton of mass \(m\) and charge \(+e\) is constrained to move along the \(x\)-axis in a region where the electric potential \(V(x)\) is shown in the graph. At position \(x = 1.0\text{ m}\), the proton has a kinetic energy of \(2.0e V_0\) and is traveling in the \(+x\)-direction. What is the maximum speed achieved by the proton during its subsequent motion?

![A Cartesian coordinate graph showing electric potential as a function of position. The horizontal axis is labeled x (m) with tick marks and numerical labels at integers 0, 1, 2, 3, 4, and 5. The vertical axis is labeled V (V_0) with tick marks and numerical labels at integers 0, 1, 2, 3, 4, and 5. A light gray rectangular grid aligns with all integer tick marks on both axes. A single solid black piecewise linear curve connects the following coordinates in order: (0, 5), (1, 3), (2, 2), (3, 4), (4, 0), and (5, 5). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604532-tNYUEL.jpg)

- **A.** \(2\sqrt{\dfrac{e V_0}{m}}\)
- **B.** \(\sqrt{\dfrac{5e V_0}{m}}\)
- **C.** \(\sqrt{\dfrac{6e V_0}{m}}\)
- **D.** \(\sqrt{\dfrac{10e V_0}{m}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124622/*