---
title: "An open cart of initial mass \\(M_0\\) is initially at rest on a frictionless horizontal surface. Sand drops vertically into the cart from a stationary overhead hopper at a constant mass rate of \\(C = \\dfrac{dm}{dt}\\). A horizontal pulling force \\(F(t)\\) is applied to the cart such that it moves in a straight line with a constant horizontal acceleration \\(a\\). Which of the following expressions represents the magnitude of the horizontal force \\(F(t)\\) required to maintain this constant acceleration as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/120759/"
date_modified: "2026-08-23T04:43:02+00:00"
---

# An open cart of initial mass \(M_0\) is initially at rest on a frictionless horizontal surface. Sand drops vertically into the cart from a stationary overhead hopper at a constant mass rate of \(C = \dfrac{dm}{dt}\). A horizontal pulling force \(F(t)\) is applied to the cart such that it moves in a straight line with a constant horizontal acceleration \(a\). Which of the following expressions represents the magnitude of the horizontal force \(F(t)\) required to maintain this constant acceleration as a function of time \(t\)?

An open cart of initial mass \(M_0\) is initially at rest on a frictionless horizontal surface. Sand drops vertically into the cart from a stationary overhead hopper at a constant mass rate of \(C = \dfrac{dm}{dt}\). A horizontal pulling force \(F(t)\) is applied to the cart such that it moves in a straight line with a constant horizontal acceleration \(a\). Which of the following expressions represents the magnitude of the horizontal force \(F(t)\) required to maintain this constant acceleration as a function of time \(t\)?

![A schematic diagram showing a horizontal frictionless track represented by a solid horizontal line. Resting on the track is an open-topped rectangular cart with two small circle wheels, labeled M_0. Directly above the open cart is a stationary funnel-shaped hopper. Vertical dashed lines with small dots drop straight down from the hopper into the cart, labeled with rate C. A horizontal arrow pointing to the right is attached to the right side of the cart, labeled F(t). Above the cart, a rightward arrow indicates the acceleration a. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460181-nliosV.jpg)

- **A.** \(F(t) = Cat\)
- **B.** \(F(t) = a(M_0 + Ct)\)
- **C.** \(F(t) = a(M_0 + 2Ct)\)
- **D.** \(F(t) = 2a(M_0 + Ct)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120759/*