---
title: "A particle of mass \\(m\\) moves along the \\(x\\)-axis under the influence of a single net force directed along the \\(x\\)-axis. The particle is released from rest at \\(x = 0\\). The force \\(F\\) as a function of position \\(x\\) is shown in the graph. Which of the following correctly ranks the speeds \\(v_1\\), \\(v_2\\), \\(v_3\\), and \\(v_4\\) of the particle at positions \\(x = 1\\text{ m}\\), \\(x = 2\\text{ m}\\), \\(x = 3\\text{ m}\\), and \\(x = 4\\text{ m}\\), respectively?"
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url: "https://nerd-notes.com/ubq/124000/"
date_modified: "2026-09-28T13:30:09+00:00"
---

# A particle of mass \(m\) moves along the \(x\)-axis under the influence of a single net force directed along the \(x\)-axis. The particle is released from rest at \(x = 0\). The force \(F\) as a function of position \(x\) is shown in the graph. Which of the following correctly ranks the speeds \(v_1\), \(v_2\), \(v_3\), and \(v_4\) of the particle at positions \(x = 1\text{ m}\), \(x = 2\text{ m}\), \(x = 3\text{ m}\), and \(x = 4\text{ m}\), respectively?

A particle of mass \(m\) moves along the \(x\)-axis under the influence of a single net force directed along the \(x\)-axis. The particle is released from rest at \(x = 0\). The force \(F\) as a function of position \(x\) is shown in the graph. Which of the following correctly ranks the speeds \(v_1\), \(v_2\), \(v_3\), and \(v_4\) of the particle at positions \(x = 1\text{ m}\), \(x = 2\text{ m}\), \(x = 3\text{ m}\), and \(x = 4\text{ m}\), respectively?

![A Cartesian coordinate graph with horizontal axis labeled x (m) ranging from 0 to 5 with integer tick marks at 0, 1, 2, 3, 4, 5, and vertical axis labeled F (N) ranging from -5 to 7 with integer tick marks every 1 unit. Light gray gridlines extend uniformly across the plotting area. A single piecewise linear curve composed of two connected straight line segments represents the force profile. The first segment starts at coordinate (0, 6) and slopes downward to coordinate (2, 0), passing through (1, 3). The second segment begins at (2, 0) and slopes downward to coordinate (4, -4), passing through (3, -2). No other curves, labels, symbols, or shaded regions appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602208-LbOOiX.jpg)

- **A.** \(v_1 > v_2 > v_3 > v_4\)
- **B.** \(v_2 > v_3 > v_1 > v_4\)
- **C.** \(v_2 > v_1 > v_3 > v_4\)
- **D.** \(v_4 > v_3 > v_2 > v_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124000/*