---
title: "A particle of mass m moves along the x-axis in a region where its potential energy U(x) is represented by the smooth, concave-up curve shown. The particle has a constant total mechanical energy E_0. Which of the following best describes the qualitative graph of the particle’s kinetic energy K as a function of position x over the classically allowed region of motion?"
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url: "https://nerd-notes.com/ubq/120658/"
date_modified: "2026-08-23T04:42:30+00:00"
---

# A particle of mass m moves along the x-axis in a region where its potential energy U(x) is represented by the smooth, concave-up curve shown. The particle has a constant total mechanical energy E_0. Which of the following best describes the qualitative graph of the particle’s kinetic energy K as a function of position x over the classically allowed region of motion?

A particle of mass m moves along the x-axis in a region where its potential energy U(x) is represented by the smooth, concave-up curve shown. The particle has a constant total mechanical energy E_0. Which of the following best describes the qualitative graph of the particle's kinetic energy K as a function of position x over the classically allowed region of motion?

![A coordinate plane with a horizontal axis labeled x and a vertical axis labeled U(x). A smooth, continuous solid curve represents potential energy U(x), forming a single smooth U-shaped well with a local minimum at x = x_m. A dashed horizontal line across the graph is labeled E_0. The dashed line intersects the solid curve at exactly two points, corresponding to x = x_1 and x = x_2, where x_1 < x_m < x_2. For x < x_1 and x > x_2, the solid curve U(x) lies strictly above the dashed line E_0. At x = x_m, the minimum point of the curve is labeled U(x_m). Vertical dashed drop lines extend downward from the intersection points to tick marks labeled x_1 and x_2 on the horizontal axis, and from the minimum to a tick mark labeled x_m. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460150-trPWfi.jpg)

- **A.** A curve that is concave up between \(x_1\) and \(x_2\), with a local minimum at \(x = x_m\) and reaching \(E_0\) at \(x = x_1\) and \(x = x_2\)
- **B.** A curve that is concave up between \(x_1\) and \(x_2\), with zeros at \(x = x_1\) and \(x = x_2\) and a local minimum at \(x = x_m\)
- **C.** A curve that is concave down between \(x_1\) and \(x_2\), with values of \(E_0\) at \(x = x_1\) and \(x = x_2\) and a local maximum at \(x = x_m\)
- **D.** A curve that is concave down between \(x_1\) and \(x_2\), with zeros at \(x = x_1\) and \(x = x_2\) and a local maximum of \(E_0 - U(x_m)\) at \(x = x_m\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120658/*