---
title: "An object of mass \\(m\\) is dropped from rest and falls vertically through a fluid. The motion of the object is governed by the differential equation \\(m \\dfrac{dv}{dt} = mg – bv\\), where \\(v\\) is the speed of the object, \\(g\\) is the acceleration due to gravity, and \\(b\\) is a positive drag constant. Which of the following expressions represents the terminal speed \\(v_T\\) of the object?"
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url: "https://nerd-notes.com/ubq/117532/"
date_modified: "2026-08-04T07:48:50+00:00"
---

# An object of mass \(m\) is dropped from rest and falls vertically through a fluid. The motion of the object is governed by the differential equation \(m \dfrac{dv}{dt} = mg – bv\), where \(v\) is the speed of the object, \(g\) is the acceleration due to gravity, and \(b\) is a positive drag constant. Which of the following expressions represents the terminal speed \(v_T\) of the object?

An object of mass \(m\) is dropped from rest and falls vertically through a fluid. The motion of the object is governed by the differential equation \(m \dfrac{dv}{dt} = mg - bv\), where \(v\) is the speed of the object, \(g\) is the acceleration due to gravity, and \(b\) is a positive drag constant. Which of the following expressions represents the terminal speed \(v_T\) of the object?

- **A.** \(\dfrac{b}{mg}\)
- **B.** \(\dfrac{mb}{g}\)
- **C.** \(\sqrt{\dfrac{mg}{b}}\)
- **D.** \(\dfrac{mg}{b}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117532/*