---
title: "A particle of mass \\(m\\) is initially at rest at position \\(x = 0\\) at time \\(t = 0\\). A net force \\(F(t)\\) directed along the \\(x\\)-axis acts on the particle as shown in the graph. The curve crosses the time axis at \\(t_1\\), and the region bounded by the curve above the time axis on the interval \\([0, t_1]\\) has an area equal in magnitude to the region below the time axis on the interval \\([t_1, t_2]\\). Which of the following statements correctly describes the motion of the particle?"
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url: "https://nerd-notes.com/ubq/124191/"
date_modified: "2026-09-28T13:31:10+00:00"
---

# A particle of mass \(m\) is initially at rest at position \(x = 0\) at time \(t = 0\). A net force \(F(t)\) directed along the \(x\)-axis acts on the particle as shown in the graph. The curve crosses the time axis at \(t_1\), and the region bounded by the curve above the time axis on the interval \([0, t_1]\) has an area equal in magnitude to the region below the time axis on the interval \([t_1, t_2]\). Which of the following statements correctly describes the motion of the particle?

A particle of mass \(m\) is initially at rest at position \(x = 0\) at time \(t = 0\). A net force \(F(t)\) directed along the \(x\)-axis acts on the particle as shown in the graph. The curve crosses the time axis at \(t_1\), and the region bounded by the curve above the time axis on the interval \([0, t_1]\) has an area equal in magnitude to the region below the time axis on the interval \([t_1, t_2]\). Which of the following statements correctly describes the motion of the particle?

![A Cartesian coordinate plane with horizontal axis labeled t and vertical axis labeled F. The axes meet at an origin labeled 0. Along the horizontal axis, two distinct positive time values are marked with tick marks labeled t_1 and t_2, with t_2 > t_1. A smooth solid curve begins on the positive vertical axis at t = 0, slopes downward to intersect the horizontal axis at t_1, reaches a smooth local minimum below the horizontal axis between t_1 and t_2, and continues below the horizontal axis past t_2. The region bounded between the curve and the horizontal axis from t = 0 to t_1 has a light gray fill. The region bounded between the curve and the horizontal axis from t_1 to t_2 has an identical light gray fill. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602270-8u3kQ0.jpg)

- **A.** The particle achieves its maximum displacement from the origin at \(t_1\) and its maximum speed at \(t_2\).
- **B.** The particle achieves its maximum speed at \(t_1\) and its maximum displacement from the origin at \(t_2\).
- **C.** The particle achieves its maximum speed at \(t_1\) and returns to the origin at \(t_2\).
- **D.** The particle momentarily comes to rest at \(t_1\) and achieves its maximum displacement from the origin at \(t_2\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124191/*