---
title: "A particle constrained to move along the x-axis is subject to a conservative force associated with the potential energy function U(x) shown in the graph. The potential energy increases linearly from U = 0 at x = 0 to U = U_0 at x = 2d, remains constant at U = U_0 from x = 2d to x = 3d, and decreases linearly from U = U_0 to U = 0 from x = 3d to x = 4d. Letting F_0 = \\dfrac{U_0}{2d}, which of the following graphs best represents the component of the net force F_x exerted on the particle as a function of position x?"
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url: "https://nerd-notes.com/ubq/124051/"
date_modified: "2026-09-28T13:30:16+00:00"
---

# A particle constrained to move along the x-axis is subject to a conservative force associated with the potential energy function U(x) shown in the graph. The potential energy increases linearly from U = 0 at x = 0 to U = U_0 at x = 2d, remains constant at U = U_0 from x = 2d to x = 3d, and decreases linearly from U = U_0 to U = 0 from x = 3d to x = 4d. Letting F_0 = \dfrac{U_0}{2d}, which of the following graphs best represents the component of the net force F_x exerted on the particle as a function of position x?

A particle constrained to move along the x-axis is subject to a conservative force associated with the potential energy function U(x) shown in the graph. The potential energy increases linearly from U = 0 at x = 0 to U = U_0 at x = 2d, remains constant at U = U_0 from x = 2d to x = 3d, and decreases linearly from U = U_0 to U = 0 from x = 3d to x = 4d. Letting F_0 = \dfrac{U_0}{2d}, which of the following graphs best represents the component of the net force F_x exerted on the particle as a function of position x?

![A Cartesian coordinate graph showing potential energy U on the vertical axis versus position x on the horizontal axis. The vertical axis has a positive tick mark labeled U_0 and an origin labeled 0. The horizontal axis has tick marks labeled 0, 2d, 3d, and 4d, with the distance from 0 to 2d twice the length of the interval from 2d to 3d and the interval from 3d to 4d. Thin dashed gray lines extend from the tick U_0 horizontally to points (2d, U_0) and (3d, U_0), and vertically down to 2d and 3d on the horizontal axis. A solid black line starts at (0, 0), rises with constant positive slope to (2d, U_0), extends horizontally from (2d, U_0) to (3d, U_0), and descends with constant negative slope from (3d, U_0) to (4d, 0). Bare axes without gridlines. No other labels, lines, text, or curves appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602215-P4U9y6.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124051/*