---
title: "A particle of mass \\(m\\) is constrained to move along the \\(x\\)-axis in a region where its potential energy \\(U(x)\\) is given by the function shown in the graph. The particle is released from rest at \\(x = x_0\\) and moves with a constant total mechanical energy \\(E_0\\). Which of the following statements correctly compares the kinetic energy \\(K\\) of the particle at positions \\(x_1\\), \\(x_3\\), and \\(x_4\\), and specifies the direction of the net force exerted on the particle at position \\(x_2\\)?"
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url: "https://nerd-notes.com/ubq/124175/"
date_modified: "2026-09-28T13:30:53+00:00"
---

# A particle of mass \(m\) is constrained to move along the \(x\)-axis in a region where its potential energy \(U(x)\) is given by the function shown in the graph. The particle is released from rest at \(x = x_0\) and moves with a constant total mechanical energy \(E_0\). Which of the following statements correctly compares the kinetic energy \(K\) of the particle at positions \(x_1\), \(x_3\), and \(x_4\), and specifies the direction of the net force exerted on the particle at position \(x_2\)?

A particle of mass \(m\) is constrained to move along the \(x\)-axis in a region where its potential energy \(U(x)\) is given by the function shown in the graph. The particle is released from rest at \(x = x_0\) and moves with a constant total mechanical energy \(E_0\). Which of the following statements correctly compares the kinetic energy \(K\) of the particle at positions \(x_1\), \(x_3\), and \(x_4\), and specifies the direction of the net force exerted on the particle at position \(x_2\)?

![A Cartesian coordinate graph with a horizontal axis labeled \(x\) and a vertical axis labeled \(U(x)\). A horizontal dashed line spans across the graph at a vertical height labeled \(E_0\). A smooth solid curve representing potential energy begins at the intersection with the dashed line at position \(x_0\). The curve decreases to a local minimum at position \(x_1\), increases with a positive slope through position \(x_2\), and reaches a local maximum at position \(x_3\) that is below the dashed line \(E_0\). The curve then decreases to a global minimum at position \(x_4\), which is visibly lower than the minimum at \(x_1\), before rising again to intersect the dashed line at position \(x_5\). Vertical dashed drop lines connect the points on the curve at \(x_0\), \(x_1\), \(x_2\), \(x_3\), \(x_4\), and \(x_5\) to their labeled tick marks along the horizontal axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602253-U0BkwS.jpg)

- **A.** The kinetic energy satisfies \(K(x_4) > K(x_1) > K(x_3)\), and the net force on the particle at \(x_2\) is directed in the negative \(x\)-direction.
- **B.** The kinetic energy satisfies \(K(x_4) > K(x_1) > K(x_3)\), and the net force on the particle at \(x_2\) is directed in the positive \(x\)-direction.
- **C.** The kinetic energy satisfies \(K(x_3) > K(x_1) > K(x_4)\), and the net force on the particle at \(x_2\) is directed in the negative \(x\)-direction.
- **D.** The kinetic energy satisfies \(K(x_3) > K(x_1) > K(x_4)\), and the net force on the particle at \(x_2\) is directed in the positive \(x\)-direction.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124175/*