---
title: "A particle moves along the x-axis while subjected to a single conservative force \\(F_x(x)\\). The force \\(F_x\\) increases linearly from \\(0 \\text{ N}\\) at \\(x = 0 \\text{ m}\\) to \\(8 \\text{ N}\\) at \\(x = 2 \\text{ m}\\), decreases linearly to \\(0 \\text{ N}\\) at \\(x = 5 \\text{ m}\\), and then decreases linearly to \\(-4 \\text{ N}\\) at \\(x = 7 \\text{ m}\\). What is the change in potential energy \\(\\Delta U\\) of the particle-system as the particle moves from \\(x = 0 \\text{ m}\\) to \\(x = 7 \\text{ m}\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/117633/"
date_modified: "2026-08-04T07:49:25+00:00"
---

# A particle moves along the x-axis while subjected to a single conservative force \(F_x(x)\). The force \(F_x\) increases linearly from \(0 \text{ N}\) at \(x = 0 \text{ m}\) to \(8 \text{ N}\) at \(x = 2 \text{ m}\), decreases linearly to \(0 \text{ N}\) at \(x = 5 \text{ m}\), and then decreases linearly to \(-4 \text{ N}\) at \(x = 7 \text{ m}\). What is the change in potential energy \(\Delta U\) of the particle-system as the particle moves from \(x = 0 \text{ m}\) to \(x = 7 \text{ m}\)?

A particle moves along the x-axis while subjected to a single conservative force \(F_x(x)\). The force \(F_x\) increases linearly from \(0 \text{ N}\) at \(x = 0 \text{ m}\) to \(8 \text{ N}\) at \(x = 2 \text{ m}\), decreases linearly to \(0 \text{ N}\) at \(x = 5 \text{ m}\), and then decreases linearly to \(-4 \text{ N}\) at \(x = 7 \text{ m}\). What is the change in potential energy \(\Delta U\) of the particle-system as the particle moves from \(x = 0 \text{ m}\) to \(x = 7 \text{ m}\)?

![A Cartesian graph of force F_x in newtons versus position x in meters. The horizontal axis is labeled x (m) with tick marks from 0 to 7 at integer intervals. The vertical axis is labeled F_x (N) with tick marks at -4, 0, 4, and 8. A solid line plot starts at the origin (0, 0), rises linearly to a peak at (2, 8), descends linearly passing through (5, 0), and continues descending linearly to terminate at (7, -4). Grid lines extend lightly from each major axis tick. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829764-RfnyL2.jpg)

- **A.** \(-16 \text{ J}\)
- **B.** \(-12 \text{ J}\)
- **C.** \(+12 \text{ J}\)
- **D.** \(+16 \text{ J}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117633/*