---
title: "A particle moves in the \\(xy\\)-plane such that its position as a function of time \\(t\\) is given by \\(\\vec{r}(t) = v_0 t\\,\\hat{i} + \\dfrac{1}{2} b t^2\\,\\hat{j}\\), where \\(v_0\\) and \\(b\\) are positive constants. Which of the following expressions represents the magnitude of the component of the particle’s acceleration perpendicular to its velocity, \\(a_\\perp(t)\\), as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/120480/"
date_modified: "2026-08-23T04:39:04+00:00"
---

# A particle moves in the \(xy\)-plane such that its position as a function of time \(t\) is given by \(\vec{r}(t) = v_0 t\,\hat{i} + \dfrac{1}{2} b t^2\,\hat{j}\), where \(v_0\) and \(b\) are positive constants. Which of the following expressions represents the magnitude of the component of the particle’s acceleration perpendicular to its velocity, \(a_\perp(t)\), as a function of time \(t\)?

A particle moves in the \(xy\)-plane such that its position as a function of time \(t\) is given by \(\vec{r}(t) = v_0 t\,\hat{i} + \dfrac{1}{2} b t^2\,\hat{j}\), where \(v_0\) and \(b\) are positive constants. Which of the following expressions represents the magnitude of the component of the particle's acceleration perpendicular to its velocity, \(a_\perp(t)\), as a function of time \(t\)?

- **A.** \(\dfrac{b v_0}{v_0 + b t}\)
- **B.** \(\dfrac{b^2 t}{\sqrt{v_0^2 + b^2 t^2}}\)
- **C.** \(\dfrac{b v_0^2}{v_0^2 + b^2 t^2}\)
- **D.** \(\dfrac{b v_0}{\sqrt{v_0^2 + b^2 t^2}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120480/*