---
title: "A cart of initial mass \\(m_0\\) moves along a straight, frictionless horizontal track at a constant speed \\(v_0\\). Rain falling vertically enters the open top of the cart such that the total mass of the cart and accumulated water increases with time according to \\(m(t) = m_0 + b t^2\\), where \\(b\\) is a positive constant. An engine exerts a horizontal force \\(F(t)\\) on the cart to maintain its constant speed. Which of the following expressions represents the magnitude of the horizontal force \\(F(t)\\) as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/117651/"
date_modified: "2026-08-04T07:49:30+00:00"
---

# A cart of initial mass \(m_0\) moves along a straight, frictionless horizontal track at a constant speed \(v_0\). Rain falling vertically enters the open top of the cart such that the total mass of the cart and accumulated water increases with time according to \(m(t) = m_0 + b t^2\), where \(b\) is a positive constant. An engine exerts a horizontal force \(F(t)\) on the cart to maintain its constant speed. Which of the following expressions represents the magnitude of the horizontal force \(F(t)\) as a function of time \(t\)?

A cart of initial mass \(m_0\) moves along a straight, frictionless horizontal track at a constant speed \(v_0\). Rain falling vertically enters the open top of the cart such that the total mass of the cart and accumulated water increases with time according to \(m(t) = m_0 + b t^2\), where \(b\) is a positive constant. An engine exerts a horizontal force \(F(t)\) on the cart to maintain its constant speed. Which of the following expressions represents the magnitude of the horizontal force \(F(t)\) as a function of time \(t\)?

![A horizontal black line representing a ground track extends across the lower portion of the image. Centered on the track is a rectangular box with an open top, labeled \(m(t)\). Attached to the bottom of the box are two small circular wheels touching the track. A horizontal arrow pointing to the right is attached to the right vertical face of the box, with its arrowhead pointing right, labeled \(F(t)\). A second horizontal arrow pointing right is drawn above the box, labeled \(v_0\). Directly above the open top of the box, exactly four vertical dashed arrows point downward toward the top opening. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829769-eVOnko.jpg)

- **A.** \(b v_0 t\)
- **B.** \(\dfrac{m_0 v_0}{t} + b v_0 t\)
- **C.** \(2b v_0 t\)
- **D.** \(\dfrac{m_0 v_0}{t} + 2b v_0 t\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117651/*