---
title: "A test vehicle moves along a horizontal circular track of radius \\(R\\). Starting from rest at time \\(t = 0\\), the vehicle’s tangential acceleration increases linearly with time according to \\(a_t(t) = ct\\), where \\(c\\) is a positive constant. Which of the following expressions represents the magnitude of the total acceleration of the vehicle as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/117535/"
date_modified: "2026-08-04T07:48:56+00:00"
---

# A test vehicle moves along a horizontal circular track of radius \(R\). Starting from rest at time \(t = 0\), the vehicle’s tangential acceleration increases linearly with time according to \(a_t(t) = ct\), where \(c\) is a positive constant. Which of the following expressions represents the magnitude of the total acceleration of the vehicle as a function of time \(t\)?

A test vehicle moves along a horizontal circular track of radius \(R\). Starting from rest at time \(t = 0\), the vehicle's tangential acceleration increases linearly with time according to \(a_t(t) = ct\), where \(c\) is a positive constant. Which of the following expressions represents the magnitude of the total acceleration of the vehicle as a function of time \(t\)?

- **A.** \(ct \left( 1 + \dfrac{c t^3}{4R} \right)\)
- **B.** \(ct \sqrt{1 + \dfrac{c^2 t^6}{R^2}}\)
- **C.** \(ct \sqrt{1 + \dfrac{c^2 t^6}{16 R^2}}\)
- **D.** \(\dfrac{c^2 t^4}{4R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117535/*