---
title: "A particle of mass \\(m\\) moves along the \\(x\\)-axis in a region where its potential energy \\(U(x)\\) varies with position as shown in the graph. The particle is subject only to the conservative force associated with this potential energy and has a constant total mechanical energy \\(E\\), represented by the horizontal dashed line.  Which of the following statements correctly describes the motion and forces acting on the particle within the region \\(x_1 \\le x \\le x_4\\)?"
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url: "https://nerd-notes.com/ubq/120682/"
date_modified: "2026-08-23T04:42:39+00:00"
---

# A particle of mass \(m\) moves along the \(x\)-axis in a region where its potential energy \(U(x)\) varies with position as shown in the graph. The particle is subject only to the conservative force associated with this potential energy and has a constant total mechanical energy \(E\), represented by the horizontal dashed line.

Which of the following statements correctly describes the motion and forces acting on the particle within the region \(x_1 \le x \le x_4\)?

A particle of mass \(m\) moves along the \(x\)-axis in a region where its potential energy \(U(x)\) varies with position as shown in the graph. The particle is subject only to the conservative force associated with this potential energy and has a constant total mechanical energy \(E\), represented by the horizontal dashed line.

Which of the following statements correctly describes the motion and forces acting on the particle within the region \(x_1 \le x \le x_4\)?

![A 2D Cartesian graph with a horizontal axis labeled x and a vertical axis labeled Energy. A horizontal dashed line spans the width of the graph at vertical value E, labeled E at the left. A smooth solid curve representing potential energy U(x) is drawn. The curve starts above E for x < x_1, slopes downward to intersect the dashed line E at position x_1, continues downward to reach a smooth local minimum at position x_2, rises to a smooth local maximum at position x_3 where U(x_3) is strictly below E, dips slightly, and then rises upward to intersect the dashed line E at position x_4. Vertical thin dotted lines drop from the points on the curve at x_1, x_2, x_3, and x_4 to tick marks labeled x_1, x_2, x_3, and x_4 on the horizontal axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-graph-1-1787460159-olfgPA.jpg)

- **A.** The particle reaches its maximum speed at \(x = x_2\) and is in stable equilibrium there because the net force is zero and the potential energy has a local minimum.
- **B.** The particle is in equilibrium at \(x = x_1\) and \(x = x_4\) because the velocity of the particle is instantaneously zero at these positions.
- **C.** Between \(x = x_1\) and \(x = x_2\), the net force on the particle is directed in the negative \(x\)-direction because the potential energy decreases with increasing position.
- **D.** At \(x = x_3\), the particle is in stable equilibrium and its kinetic energy is zero because the curve has a horizontal tangent.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120682/*