---
title: "The position of a particle moving in the \\(xy\\)-plane as a function of time \\(t\\) is given by the vector equation \\(\\vec{r}(t) = (b t^2)\\hat{i} + (c t)\\hat{j}\\), where \\(b\\) and \\(c\\) are positive constants with appropriate SI units. Which of the following expressions represents the speed of the particle as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/117545/"
date_modified: "2026-08-04T07:48:58+00:00"
---

# The position of a particle moving in the \(xy\)-plane as a function of time \(t\) is given by the vector equation \(\vec{r}(t) = (b t^2)\hat{i} + (c t)\hat{j}\), where \(b\) and \(c\) are positive constants with appropriate SI units. Which of the following expressions represents the speed of the particle as a function of time \(t\)?

The position of a particle moving in the \(xy\)-plane as a function of time \(t\) is given by the vector equation \(\vec{r}(t) = (b t^2)\hat{i} + (c t)\hat{j}\), where \(b\) and \(c\) are positive constants with appropriate SI units. Which of the following expressions represents the speed of the particle as a function of time \(t\)?

- **A.** \(2b t + c\)
- **B.** \(\sqrt{b^2 t^2 + c^2}\)
- **C.** \(\sqrt{4b^2 t^2 + c^2}\)
- **D.** \(\sqrt{2b^2 t^2 + c^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117545/*