---
title: "A block of mass \\(M\\) is placed on a rough horizontal surface with a coefficient of kinetic friction \\(\\mu_k\\). At time \\(t = 0\\), the block is pulled from rest by a string that exerts a constant force of magnitude \\(F\\) at an angle \\(\\theta\\) above the horizontal. The block remains in contact with the surface throughout the motion, and the horizontal component of the applied force is greater than the force of kinetic friction. Which of the following expressions correctly represents the horizontal displacement \\(d\\) of the block as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/114627/"
date_modified: "2026-07-03T04:46:35+00:00"
---

# A block of mass \(M\) is placed on a rough horizontal surface with a coefficient of kinetic friction \(\mu_k\). At time \(t = 0\), the block is pulled from rest by a string that exerts a constant force of magnitude \(F\) at an angle \(\theta\) above the horizontal. The block remains in contact with the surface throughout the motion, and the horizontal component of the applied force is greater than the force of kinetic friction. Which of the following expressions correctly represents the horizontal displacement \(d\) of the block as a function of time \(t\)?

A block of mass \(M\) is placed on a rough horizontal surface with a coefficient of kinetic friction \(\mu_k\). At time \(t = 0\), the block is pulled from rest by a string that exerts a constant force of magnitude \(F\) at an angle \(\theta\) above the horizontal. The block remains in contact with the surface throughout the motion, and the horizontal component of the applied force is greater than the force of kinetic friction. Which of the following expressions correctly represents the horizontal displacement \(d\) of the block as a function of time \(t\)?

![A rectangular block of mass M on a horizontal line. A vector arrow labeled F originates from the center of the block and points diagonally upward and to the right, making an angle theta with the horizontal. A frictional force vector points to the left.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1783053995-Zbnlln.jpg)

- **A.** \(d = \dfrac{t^2}{2M} [F\cos\theta - \mu_k Mg]\)
- **B.** \(d = \dfrac{t^2}{2M} [F(\cos\theta - \mu_k\sin\theta) - \mu_k Mg]\)
- **C.** \(d = \dfrac{t^2}{2M} [F(\cos\theta + \mu_k\sin\theta) - \mu_k Mg]\)
- **D.** \(d = \dfrac{t^2}{2M} [F(\sin\theta + \mu_k\cos\theta) - \mu_k Mg]\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114627/*