---
title: "A cart of mass \\(m\\) moves along a straight, frictionless horizontal track. A net external force acts on the cart along its line of motion such that the magnitude of the cart’s linear momentum increases by a factor of \\(3\\). What is the ratio of the cart’s initial kinetic energy to its final kinetic energy, \\(\\dfrac{K_i}{K_f}\\)?"
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url: "https://nerd-notes.com/ubq/120626/"
date_modified: "2026-08-23T04:42:11+00:00"
---

# A cart of mass \(m\) moves along a straight, frictionless horizontal track. A net external force acts on the cart along its line of motion such that the magnitude of the cart’s linear momentum increases by a factor of \(3\). What is the ratio of the cart’s initial kinetic energy to its final kinetic energy, \(\dfrac{K_i}{K_f}\)?

A cart of mass \(m\) moves along a straight, frictionless horizontal track. A net external force acts on the cart along its line of motion such that the magnitude of the cart's linear momentum increases by a factor of \(3\). What is the ratio of the cart's initial kinetic energy to its final kinetic energy, \(\dfrac{K_i}{K_f}\)?

- **A.** \(\dfrac{1}{9}\)
- **B.** \(\dfrac{1}{3}\)
- **C.** \(3\)
- **D.** \(9\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120626/*