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title: "A cart of mass \\(M\\) moves with initial speed \\(v_0\\) along a horizontal frictionless track toward an identical cart of mass \\(M\\) that is initially at rest. The two carts collide and stick together. What is the ratio of the total kinetic energy of the two-cart system after the collision to the total kinetic energy of the system before the collision, \\(\\dfrac{K_f}{K_i}\\)?"
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url: "https://nerd-notes.com/ubq/120715/"
date_modified: "2026-08-23T04:42:49+00:00"
---

# A cart of mass \(M\) moves with initial speed \(v_0\) along a horizontal frictionless track toward an identical cart of mass \(M\) that is initially at rest. The two carts collide and stick together. What is the ratio of the total kinetic energy of the two-cart system after the collision to the total kinetic energy of the system before the collision, \(\dfrac{K_f}{K_i}\)?

A cart of mass \(M\) moves with initial speed \(v_0\) along a horizontal frictionless track toward an identical cart of mass \(M\) that is initially at rest. The two carts collide and stick together. What is the ratio of the total kinetic energy of the two-cart system after the collision to the total kinetic energy of the system before the collision, \(\dfrac{K_f}{K_i}\)?

![A horizontal track is shown as a flat straight line. On the left, a rectangular cart of mass M moves to the right with a horizontal arrow above it labeled v_0. On the right, a second identical rectangular cart of mass M is at rest, labeled v = 0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460169-nStMSq.jpg)

- **A.** \(\dfrac{1}{4}\)
- **B.** \(\dfrac{1}{2}\)
- **C.** \(\dfrac{3}{4}\)
- **D.** \(1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120715/*