---
title: "A particle moves along the \\(x\\)-axis with an instantaneous velocity given by the function \\(v_x(t) = 3t^2 – 12t\\), where \\(v_x\\) is in meters per second and \\(t\\) is in seconds. The particle’s motion is observed over the time interval from \\(t = 0\\text{ s}\\) to \\(t = 5\\text{ s}\\). Which of the following correctly identifies the direction of the particle’s average velocity vector and the relationship between its average speed \\(s_{\\text{avg}}\\) and the magnitude of its average velocity \\(|\\vec{v}_{\\text{avg}}|\\) over this interval?"
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url: "https://nerd-notes.com/ubq/120490/"
date_modified: "2026-08-23T04:39:08+00:00"
---

# A particle moves along the \(x\)-axis with an instantaneous velocity given by the function \(v_x(t) = 3t^2 – 12t\), where \(v_x\) is in meters per second and \(t\) is in seconds. The particle’s motion is observed over the time interval from \(t = 0\text{ s}\) to \(t = 5\text{ s}\). Which of the following correctly identifies the direction of the particle’s average velocity vector and the relationship between its average speed \(s_{\text{avg}}\) and the magnitude of its average velocity \(|\vec{v}_{\text{avg}}|\) over this interval?

A particle moves along the \(x\)-axis with an instantaneous velocity given by the function \(v_x(t) = 3t^2 - 12t\), where \(v_x\) is in meters per second and \(t\) is in seconds. The particle's motion is observed over the time interval from \(t = 0\text{ s}\) to \(t = 5\text{ s}\). Which of the following correctly identifies the direction of the particle's average velocity vector and the relationship between its average speed \(s_{\text{avg}}\) and the magnitude of its average velocity \(|\vec{v}_{\text{avg}}|\) over this interval?

- **A.** Directed in the \(+x\)-direction, and \(s_{\text{avg}} = |\vec{v}_{\text{avg}}|\)
- **B.** Directed in the \(+x\)-direction, and \(s_{\text{avg}} > |\vec{v}_{\text{avg}}|\)
- **C.** Directed in the \(-x\)-direction, and \(s_{\text{avg}} > |\vec{v}_{\text{avg}}|\)
- **D.** Directed in the \(-x\)-direction, and \(s_{\text{avg}} = |\vec{v}_{\text{avg}}|\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120490/*