---
title: "A boat of mass \\(m\\) coasts along a straight horizontal line on a calm lake. At time \\(t = 0\\), the engine is turned off when the boat has an initial speed \\(v_0\\). The boat experiences a drag force from the water of magnitude \\(F_d = b v^2\\), where \\(b\\) is a positive constant and \\(v\\) is the speed of the boat. Which of the following expressions gives the speed \\(v(t)\\) of the boat as a function of time \\(t\\) for \\(t \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/117551/"
date_modified: "2026-08-04T07:49:00+00:00"
---

# A boat of mass \(m\) coasts along a straight horizontal line on a calm lake. At time \(t = 0\), the engine is turned off when the boat has an initial speed \(v_0\). The boat experiences a drag force from the water of magnitude \(F_d = b v^2\), where \(b\) is a positive constant and \(v\) is the speed of the boat. Which of the following expressions gives the speed \(v(t)\) of the boat as a function of time \(t\) for \(t \ge 0\)?

A boat of mass \(m\) coasts along a straight horizontal line on a calm lake. At time \(t = 0\), the engine is turned off when the boat has an initial speed \(v_0\). The boat experiences a drag force from the water of magnitude \(F_d = b v^2\), where \(b\) is a positive constant and \(v\) is the speed of the boat. Which of the following expressions gives the speed \(v(t)\) of the boat as a function of time \(t\) for \(t \ge 0\)?

- **A.** \(v(t) = v_0 e^{-\dfrac{b v_0}{m} t}\)
- **B.** \(v(t) = v_0 \left(1 - \dfrac{b v_0}{m} t\right)\)
- **C.** \(v(t) = \dfrac{v_0}{1 - \dfrac{b v_0}{m} t}\)
- **D.** \(v(t) = \dfrac{v_0}{1 + \dfrac{b v_0}{m} t}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117551/*