---
title: "A crate of mass \\(m\\) is at rest on a horizontal surface where the coefficient of static friction is \\(\\mu_s\\) and the coefficient of kinetic friction is \\(\\mu_k\\). An external horizontal force \\(F\\) is applied to the crate and its magnitude is slowly increased until the crate just begins to slide. If the force \\(F\\) is maintained at this constant threshold value once the crate is in motion, which of the following describes the crate’s motion and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/109257/"
date_modified: "2026-03-21T18:52:07+00:00"
---

# A crate of mass \(m\) is at rest on a horizontal surface where the coefficient of static friction is \(\mu_s\) and the coefficient of kinetic friction is \(\mu_k\). An external horizontal force \(F\) is applied to the crate and its magnitude is slowly increased until the crate just begins to slide. If the force \(F\) is maintained at this constant threshold value once the crate is in motion, which of the following describes the crate’s motion and provides the correct justification?

A crate of mass \(m\) is at rest on a horizontal surface where the coefficient of static friction is \(\mu_s\) and the coefficient of kinetic friction is \(\mu_k\). An external horizontal force \(F\) is applied to the crate and its magnitude is slowly increased until the crate just begins to slide. If the force \(F\) is maintained at this constant threshold value once the crate is in motion, which of the following describes the crate’s motion and provides the correct justification?

![A square crate on a flat horizontal line. A vector arrow labeled F points to the right from the center of the crate. A dashed vector arrow labeled f points to the left from the bottom of the crate where it contacts the surface.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-setup-1-1774119127-52ynkC.jpg)

- **A.** The crate moves with constant velocity because the applied force is equal to the friction force required to initiate motion.
- **B.** The crate moves with a constant, non-zero acceleration because the applied force is greater than the kinetic friction force.
- **C.** The crate moves with an increasing acceleration because the kinetic friction force decreases as the speed of the crate increases.
- **D.** The crate moves with a constant, non-zero acceleration because the normal force increases once the crate is in motion.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109257/*