---
title: "Two carts, Cart 1 and Cart 2, move along a horizontal frictionless track and undergo a one-dimensional collision along the x-axis. The graph shows the velocity v of each cart as a function of time t before, during, and after the collision. No net external horizontal force acts on the two-cart system. Which of the following statements correctly relates the inertial masses of the carts and characterizes the collision?"
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url: "https://nerd-notes.com/ubq/120748/"
date_modified: "2026-08-23T04:42:58+00:00"
---

# Two carts, Cart 1 and Cart 2, move along a horizontal frictionless track and undergo a one-dimensional collision along the x-axis. The graph shows the velocity v of each cart as a function of time t before, during, and after the collision. No net external horizontal force acts on the two-cart system. Which of the following statements correctly relates the inertial masses of the carts and characterizes the collision?

Two carts, Cart 1 and Cart 2, move along a horizontal frictionless track and undergo a one-dimensional collision along the x-axis. The graph shows the velocity v of each cart as a function of time t before, during, and after the collision. No net external horizontal force acts on the two-cart system. Which of the following statements correctly relates the inertial masses of the carts and characterizes the collision?

![A 2D line graph with a horizontal axis labeled t (s) spanning from 0 to 6 with tick marks every 1 unit, and a vertical axis labeled v (m/s) spanning from -2 to 6 with tick marks every 1 unit. A dashed horizontal line represents v = 0. Two distinct curves are plotted. A solid curve labeled Cart 1 starts at (0, 6), remains horizontal at v = 6 until t = 2, slopes downward linearly from (2, 6) to (4, 0), and remains horizontal at v = 0 from t = 4 to t = 6. A dashed curve labeled Cart 2 starts at (0, 0), remains horizontal at v = 0 until t = 2, slopes upward linearly from (2, 0) to (4, 2), and remains horizontal at v = 2 from t = 4 to t = 6. Light dotted gridlines align with each integer tick mark on both axes. No other lines, labels, text, or markings appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460178-QF84nM.jpg)

- **A.** The inertial mass of Cart 1 is three times the inertial mass of Cart 2, and the collision is inelastic because kinetic energy is dissipated.
- **B.** The magnitude of the impulse delivered to Cart 1 is three times the magnitude of the impulse delivered to Cart 2, and the collision is inelastic.
- **C.** The inertial mass of Cart 1 is one-third the inertial mass of Cart 2, and the collision is elastic because the total momentum of the system is conserved.
- **D.** The inertial mass of Cart 1 is one-third the inertial mass of Cart 2, and the collision is inelastic because the total kinetic energy of the system decreases.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120748/*