---
title: "Two blocks of masses \\(m_1\\) and \\(m_2\\) lie on a horizontal, frictionless surface and are connected by a light spring. The system is initially at rest. Starting at time \\(t = 0\\), a time-dependent horizontal external force \\(F(t) = bt\\), where \\(b\\) is a positive constant, acts on mass \\(m_1\\) to the left. What is the speed of the center of mass of the two-block system at time \\(t = T\\)?"
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url: "https://nerd-notes.com/ubq/117591/"
date_modified: "2026-08-04T07:49:14+00:00"
---

# Two blocks of masses \(m_1\) and \(m_2\) lie on a horizontal, frictionless surface and are connected by a light spring. The system is initially at rest. Starting at time \(t = 0\), a time-dependent horizontal external force \(F(t) = bt\), where \(b\) is a positive constant, acts on mass \(m_1\) to the left. What is the speed of the center of mass of the two-block system at time \(t = T\)?

Two blocks of masses \(m_1\) and \(m_2\) lie on a horizontal, frictionless surface and are connected by a light spring. The system is initially at rest. Starting at time \(t = 0\), a time-dependent horizontal external force \(F(t) = bt\), where \(b\) is a positive constant, acts on mass \(m_1\) to the left. What is the speed of the center of mass of the two-block system at time \(t = T\)?

![A horizontal line represents a frictionless surface. Two rectangular blocks labeled m_1 on the left and m_2 on the right sit on the surface. A horizontal spring connects the right side of m_1 to the left side of m_2. A horizontal arrow labeled F(t) points to the left from the left side of m_1. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-diagram-1785829753-PYqIYW.jpg)

- **A.** \(\dfrac{b T^2}{2 m_1}\)
- **B.** \(\dfrac{b T^2}{m_1 + m_2}\)
- **C.** \(\dfrac{2 b T^2}{m_1 + m_2}\)
- **D.** \(\dfrac{b T^2}{2(m_1 + m_2)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117591/*