---
title: "A block of mass \\(m\\) is placed on a horizontal track covered in a lubricant that exerts a resistive force of magnitude \\(F_r = bv\\), where \\(b\\) is a positive constant and \\(v\\) is the speed of the block. The block is pulled from rest by a constant horizontal force of magnitude \\(F_0\\). Let \\(v_T\\) be the terminal speed of the block as it moves along the track. Which of the following expressions represents the magnitude of the block’s acceleration at the instant its speed is \\(“\\dfrac{1}{4} v_T\\)?"
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url: "https://nerd-notes.com/ubq/115995/"
date_modified: "2026-08-03T07:15:52+00:00"
---

# A block of mass \(m\) is placed on a horizontal track covered in a lubricant that exerts a resistive force of magnitude \(F_r = bv\), where \(b\) is a positive constant and \(v\) is the speed of the block. The block is pulled from rest by a constant horizontal force of magnitude \(F_0\). Let \(v_T\) be the terminal speed of the block as it moves along the track. Which of the following expressions represents the magnitude of the block’s acceleration at the instant its speed is \(“\dfrac{1}{4} v_T\)?

A block of mass \(m\) is placed on a horizontal track covered in a lubricant that exerts a resistive force of magnitude \(F_r = bv\), where \(b\) is a positive constant and \(v\) is the speed of the block. The block is pulled from rest by a constant horizontal force of magnitude \(F_0\). Let \(v_T\) be the terminal speed of the block as it moves along the track. Which of the following expressions represents the magnitude of the block's acceleration at the instant its speed is \(\dfrac{1}{4} v_T\)?

![A block of mass m on a horizontal surface. A vector arrow labeled F_0 points to the right. A vector arrow labeled bv points to the left. The surface is labeled as a lubricated track.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-diag-1-1785741351-QHBjbf.jpg)

- **A.** \(\dfrac{F_0}{4m}\)
- **B.** \(\dfrac{F_0}{2m}\)
- **C.** \(\dfrac{3F_0}{4m}\)
- **D.** \(\dfrac{F_0}{m}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/115995/*