---
title: "An autonomous underwater vehicle moves along a straight horizontal path with an initial speed \\(v_0\\). At time \\(t = 0\\), its propulsion system turns off, and it experiences a resistive acceleration given by \\(a = -k v^2\\), where \\(k\\) is a positive constant with units of \\(\\text{m}^{-1}\\) and \\(v\\) is the instantaneous speed. Which of the following expressions represents the time interval \\(\\Delta t\\) required for the vehicle’s speed to decrease from \\(v_0\\) to \\(\\dfrac{v_0}{3}\\)?"
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url: "https://nerd-notes.com/ubq/117601/"
date_modified: "2026-08-04T07:49:16+00:00"
---

# An autonomous underwater vehicle moves along a straight horizontal path with an initial speed \(v_0\). At time \(t = 0\), its propulsion system turns off, and it experiences a resistive acceleration given by \(a = -k v^2\), where \(k\) is a positive constant with units of \(\text{m}^{-1}\) and \(v\) is the instantaneous speed. Which of the following expressions represents the time interval \(\Delta t\) required for the vehicle’s speed to decrease from \(v_0\) to \(\dfrac{v_0}{3}\)?

An autonomous underwater vehicle moves along a straight horizontal path with an initial speed \(v_0\). At time \(t = 0\), its propulsion system turns off, and it experiences a resistive acceleration given by \(a = -k v^2\), where \(k\) is a positive constant with units of \(\text{m}^{-1}\) and \(v\) is the instantaneous speed. Which of the following expressions represents the time interval \(\Delta t\) required for the vehicle's speed to decrease from \(v_0\) to \(\dfrac{v_0}{3}\)?

- **A.** \(\Delta t = \dfrac{\ln 3}{k v_0}\)
- **B.** \(\Delta t = \dfrac{3}{2 k v_0}\)
- **C.** \(\Delta t = \dfrac{4}{k v_0}\)
- **D.** \(\Delta t = \dfrac{2}{k v_0}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117601/*