---
title: "A particle moves in the \\(xy\\)-plane such that its position vector as a function of time \\(t\\) is given by \\(\\vec{r}(t) = b\\cos(\\omega t)\\hat{i} + c\\sin(\\omega t)\\hat{j}\\), where \\(b\\), \\(c\\), and \\(\\omega\\) are positive constants with \\(b > c\\). Which row in the table correctly identifies the locations on the particle’s trajectory where its speed is greatest and describes the direction of its acceleration vector?  | | Location of Greatest Speed | Direction of Acceleration Vector | | :— | :— | :— | | A | Points on the \\(x\\)-axis | Not always directed toward the origin | | B | Points on the \\(x\\)-axis | Always directed toward the origin | | C | Points on the \\(y\\)-axis | Not always directed toward the origin | | D | Points on the \\(y\\)-axis | Always directed toward the origin |"
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url: "https://nerd-notes.com/ubq/124059/"
date_modified: "2026-09-28T13:30:18+00:00"
---

# A particle moves in the \(xy\)-plane such that its position vector as a function of time \(t\) is given by \(\vec{r}(t) = b\cos(\omega t)\hat{i} + c\sin(\omega t)\hat{j}\), where \(b\), \(c\), and \(\omega\) are positive constants with \(b > c\). Which row in the table correctly identifies the locations on the particle’s trajectory where its speed is greatest and describes the direction of its acceleration vector?

| | Location of Greatest Speed | Direction of Acceleration Vector |
| :— | :— | :— |
| A | Points on the \(x\)-axis | Not always directed toward the origin |
| B | Points on the \(x\)-axis | Always directed toward the origin |
| C | Points on the \(y\)-axis | Not always directed toward the origin |
| D | Points on the \(y\)-axis | Always directed toward the origin |

A particle moves in the \(xy\)-plane such that its position vector as a function of time \(t\) is given by \(\vec{r}(t) = b\cos(\omega t)\hat{i} + c\sin(\omega t)\hat{j}\), where \(b\), \(c\), and \(\omega\) are positive constants with \(b > c\). Which row in the table correctly identifies the locations on the particle's trajectory where its speed is greatest and describes the direction of its acceleration vector?

| | Location of Greatest Speed | Direction of Acceleration Vector |
| :--- | :--- | :--- |
| A | Points on the \(x\)-axis | Not always directed toward the origin |
| B | Points on the \(x\)-axis | Always directed toward the origin |
| C | Points on the \(y\)-axis | Not always directed toward the origin |
| D | Points on the \(y\)-axis | Always directed toward the origin |

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124059/*