---
title: "A particle constrained to move along the \\(x\\)-axis is subject to a single conservative force described by the potential energy function \\(U(x)\\). At position \\(x = x_0\\), the potential energy is zero (\\(U(x_0) = 0\\)), yet the particle experiences a non-zero instantaneous acceleration as it passes through this position. Which of the following statements provides the correct physical explanation for this observation?"
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url: "https://nerd-notes.com/ubq/123976/"
date_modified: "2026-09-28T13:29:48+00:00"
---

# A particle constrained to move along the \(x\)-axis is subject to a single conservative force described by the potential energy function \(U(x)\). At position \(x = x_0\), the potential energy is zero (\(U(x_0) = 0\)), yet the particle experiences a non-zero instantaneous acceleration as it passes through this position. Which of the following statements provides the correct physical explanation for this observation?

A particle constrained to move along the \(x\)-axis is subject to a single conservative force described by the potential energy function \(U(x)\). At position \(x = x_0\), the potential energy is zero (\(U(x_0) = 0\)), yet the particle experiences a non-zero instantaneous acceleration as it passes through this position. Which of the following statements provides the correct physical explanation for this observation?

![A bare Cartesian coordinate system showing potential energy U on the vertical axis and position x on the horizontal axis. A single smooth, solid curve represents U(x). The curve crosses the horizontal axis at a point labeled x_0 with a steep negative slope, passing continuously from positive values of U for x less than x_0 to negative values of U for x greater than x_0. A solid dot marks the intersection point at (x_0, 0). The origin is labeled O. No other labels, gridlines, arrows, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602188-B3CC6z.jpg)

- **A.** The particle accelerates because the total mechanical energy has been fully converted into kinetic energy at the zero-crossing, which inherently maximizes the particle's speed and forces its acceleration to be non-zero.
- **B.** The particle accelerates because the net force is determined by the total work accumulated along the path, which corresponds to the definite integral of the potential energy function from the reference point to \(x_0\).
- **C.** The particle accelerates because any location where the potential energy equals zero constitutes an unstable equilibrium, causing the slightest disturbance from the zero-crossing to generate a divergent net force away from that position.
- **D.** The particle accelerates because the conservative force is given by the negative spatial derivative \(F_x = -\dfrac{dU}{dx}\), meaning the acceleration depends on the local slope of the potential energy function rather than its absolute value.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123976/*