---
title: "Two blocks of masses \\(m_1\\) and \\(m_2\\) slide to the right along a horizontal surface with a uniform coefficient of kinetic friction \\(\\mu\\). Block 1 is initially traveling faster than block 2 and catches up to it, colliding and sticking to block 2 at time \\(t_c\\). The combined blocks continue sliding to the right until coming to rest at time \\(t_f\\). Which of the following graphs best represents the position of the center of mass of the two-block system, \\(x_{\\text{cm}}\\), as a function of time \\(t\\) between \\(t = 0\\) and \\(t_f\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120768/"
date_modified: "2026-08-23T04:43:09+00:00"
---

# Two blocks of masses \(m_1\) and \(m_2\) slide to the right along a horizontal surface with a uniform coefficient of kinetic friction \(\mu\). Block 1 is initially traveling faster than block 2 and catches up to it, colliding and sticking to block 2 at time \(t_c\). The combined blocks continue sliding to the right until coming to rest at time \(t_f\). Which of the following graphs best represents the position of the center of mass of the two-block system, \(x_{\text{cm}}\), as a function of time \(t\) between \(t = 0\) and \(t_f\)?

Two blocks of masses \(m_1\) and \(m_2\) slide to the right along a horizontal surface with a uniform coefficient of kinetic friction \(\mu\). Block 1 is initially traveling faster than block 2 and catches up to it, colliding and sticking to block 2 at time \(t_c\). The combined blocks continue sliding to the right until coming to rest at time \(t_f\). Which of the following graphs best represents the position of the center of mass of the two-block system, \(x_{\text{cm}}\), as a function of time \(t\) between \(t = 0\) and \(t_f\)?

- **A.** A single continuous curve that is concave down with constant curvature across the entire interval from \(t = 0\) to \(t_f\)
- **B.** A concave-down curve with an abrupt decrease in slope at \(t_c\), followed by a shallower concave-down curve until \(t_f\)
- **C.** Two connected straight line segments with a constant positive slope before \(t_c\) and a smaller constant positive slope after \(t_c\)
- **D.** A concave-down curve whose curvature abruptly becomes significantly steeper after \(t_c\) until reaching a horizontal tangent at \(t_f\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120768/*