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title: "Two blocks of masses \\(m\\) and \\(2m\\) are placed on a horizontal surface where the coefficient of kinetic friction between each block and the surface is \\(\\mu_k\\). A compressed ideal spring between the blocks is released at time \\(t = 0\\), causing the block of mass \\(m\\) to move to the left with initial speed \\(2v_0\\) and the block of mass \\(2m\\) to move to the right with initial speed \\(v_0\\). The spring detaches immediately after release, and the blocks slide along the surface until both come to rest. Defining the positive direction to the right, which of the following best describes the shape of the graph of the velocity of the center of mass, \\(v_{cm}\\), of the two-block system as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/120756/"
date_modified: "2026-08-23T04:43:01+00:00"
---

# Two blocks of masses \(m\) and \(2m\) are placed on a horizontal surface where the coefficient of kinetic friction between each block and the surface is \(\mu_k\). A compressed ideal spring between the blocks is released at time \(t = 0\), causing the block of mass \(m\) to move to the left with initial speed \(2v_0\) and the block of mass \(2m\) to move to the right with initial speed \(v_0\). The spring detaches immediately after release, and the blocks slide along the surface until both come to rest. Defining the positive direction to the right, which of the following best describes the shape of the graph of the velocity of the center of mass, \(v_{cm}\), of the two-block system as a function of time \(t\)?

Two blocks of masses \(m\) and \(2m\) are placed on a horizontal surface where the coefficient of kinetic friction between each block and the surface is \(\mu_k\). A compressed ideal spring between the blocks is released at time \(t = 0\), causing the block of mass \(m\) to move to the left with initial speed \(2v_0\) and the block of mass \(2m\) to move to the right with initial speed \(v_0\). The spring detaches immediately after release, and the blocks slide along the surface until both come to rest. Defining the positive direction to the right, which of the following best describes the shape of the graph of the velocity of the center of mass, \(v_{cm}\), of the two-block system as a function of time \(t\)?

![A horizontal ground line represents a rough surface. On the surface, two rectangular blocks rest side by side with a coiled horizontal spring compressed between them. The left block is labeled \(m\) and has a horizontal arrow pointing to the left labeled \(2v_0\). The right block is wider, labeled \(2m\), and has a horizontal arrow pointing to the right labeled \(v_0\). A single horizontal axis arrow pointing to the right is labeled \(+x\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460180-xRih54.jpg)

- **A.** A horizontal line along \(v_{cm} = 0\) for all \(t \ge 0\)
- **B.** A line with a constant negative slope from \(v_{cm} = 0\) to a minimum negative value, followed by a horizontal line remaining at that negative value
- **C.** A downward-opening parabolic curve that starts at \(v_{cm} = 0\), smoothly reaches a minimum negative value, and smoothly returns to zero
- **D.** A piecewise linear curve that decreases with a constant negative slope from \(v_{cm} = 0\) to a minimum negative value, then increases with a constant positive slope back to zero, remaining at zero thereafter

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120756/*