---
title: "A particle moves along the \\(x\\)-axis with an initial velocity \\(v(0) = v_0 > 0\\). For times \\(t \\ge 0\\), the particle experiences an acceleration given by \\(a(t) = -bt\\), where \\(b\\) is a positive constant. Which of the following graphs best represents the particle’s velocity \\(v\\) as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/124198/"
date_modified: "2026-09-28T13:31:14+00:00"
---

# A particle moves along the \(x\)-axis with an initial velocity \(v(0) = v_0 > 0\). For times \(t \ge 0\), the particle experiences an acceleration given by \(a(t) = -bt\), where \(b\) is a positive constant. Which of the following graphs best represents the particle’s velocity \(v\) as a function of time \(t\)?

A particle moves along the \(x\)-axis with an initial velocity \(v(0) = v_0 > 0\). For times \(t \ge 0\), the particle experiences an acceleration given by \(a(t) = -bt\), where \(b\) is a positive constant. Which of the following graphs best represents the particle's velocity \(v\) as a function of time \(t\)?

- **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/124198/*