---
title: "A cart with initial total mass \\(m_0\\) moves along a horizontal, frictionless track at a constant speed \\(v_0\\). Sand leaks out through a hole in the bottom of the cart at a constant mass rate \\(\\alpha\\), such that the mass of the cart and its remaining contents as a function of time is given by \\(m(t) = m_0 – \\alpha t\\). Which of the following expressions represents the magnitude of the rate of change of linear momentum \\(\\left|\\dfrac{dp}{dt}\\right|\\) of the cart and its remaining contents?"
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url: "https://nerd-notes.com/ubq/117542/"
date_modified: "2026-08-04T07:48:58+00:00"
---

# A cart with initial total mass \(m_0\) moves along a horizontal, frictionless track at a constant speed \(v_0\). Sand leaks out through a hole in the bottom of the cart at a constant mass rate \(\alpha\), such that the mass of the cart and its remaining contents as a function of time is given by \(m(t) = m_0 – \alpha t\). Which of the following expressions represents the magnitude of the rate of change of linear momentum \(\left|\dfrac{dp}{dt}\right|\) of the cart and its remaining contents?

A cart with initial total mass \(m_0\) moves along a horizontal, frictionless track at a constant speed \(v_0\). Sand leaks out through a hole in the bottom of the cart at a constant mass rate \(\alpha\), such that the mass of the cart and its remaining contents as a function of time is given by \(m(t) = m_0 - \alpha t\). Which of the following expressions represents the magnitude of the rate of change of linear momentum \(\left|\dfrac{dp}{dt}\right|\) of the cart and its remaining contents?

- **A.** \(\dfrac{m_0 v_0}{t}\)
- **B.** \((m_0 - \alpha t) v_0\)
- **C.** \(\alpha v_0 t\)
- **D.** \(\alpha v_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117542/*