---
title: "Two carts, Cart 1 of mass \\(m_1 = 2.0 \\text{ kg}\\) and Cart 2 of mass \\(m_2 = 1.0 \\text{ kg}\\), move along a horizontal, frictionless track parallel to an \\(x\\)-axis. The position \\(x\\) of each cart as a function of time \\(t\\) before, during, and after a collision is shown in the graph. Which of the following statements correctly describes the velocity of the center of mass of the two-cart system over the interval \\(0 \\le t \\le 4.0 \\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/124279/"
date_modified: "2026-09-28T14:04:38+00:00"
---

# Two carts, Cart 1 of mass \(m_1 = 2.0 \text{ kg}\) and Cart 2 of mass \(m_2 = 1.0 \text{ kg}\), move along a horizontal, frictionless track parallel to an \(x\)-axis. The position \(x\) of each cart as a function of time \(t\) before, during, and after a collision is shown in the graph. Which of the following statements correctly describes the velocity of the center of mass of the two-cart system over the interval \(0 \le t \le 4.0 \text{ s}\)?

Two carts, Cart 1 of mass \(m_1 = 2.0 \text{ kg}\) and Cart 2 of mass \(m_2 = 1.0 \text{ kg}\), move along a horizontal, frictionless track parallel to an \(x\)-axis. The position \(x\) of each cart as a function of time \(t\) before, during, and after a collision is shown in the graph. Which of the following statements correctly describes the velocity of the center of mass of the two-cart system over the interval \(0 \le t \le 4.0 \text{ s}\)?

![A Cartesian graph with time t in seconds on the horizontal axis and position x in meters on the vertical axis. The horizontal axis is labeled 't (s)' with tick marks at intervals of 1.0 from 0 to 4.0. The vertical axis is labeled 'x (m)' with tick marks at intervals of 2.0 from 0 to 10.0. Light gray gridlines align with all axis ticks. A solid line labeled 'Cart 1' begins at (0, 0), extends linearly with a positive slope to (2.0, 4.0), and continues as a horizontal line from (2.0, 4.0) to (4.0, 4.0). A dashed line labeled 'Cart 2' begins at (0, 6.0), extends linearly with a negative slope to (2.0, 4.0), and then extends linearly with a steep positive slope from (2.0, 4.0) to (4.0, 10.0). No other curves, labels, or shaded regions appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604278-IQru6K.jpg)

- **A.** The velocity of the center of mass decreases to \(0 \text{ m/s}\) at \(t = 2.0 \text{ s}\) because the two position-versus-time graphs intersect, indicating that the carts momentarily come to rest.
- **B.** The velocity of the center of mass remains constant at \(+1.0 \text{ m/s}\) throughout the interval because the mass-weighted sum of the slopes of the position-versus-time graphs is unchanged by the collision.
- **C.** The velocity of the center of mass increases from \(+0.5 \text{ m/s}\) to \(+1.5 \text{ m/s}\) at \(t = 2.0 \text{ s}\) because the unweighted average of the slopes of the position-versus-time graphs increases after the collision.
- **D.** The velocity of the center of mass increases at \(t = 2.0 \text{ s}\) because the slope of Cart 2's position-versus-time graph increases by \(4.0 \text{ m/s}\) while the slope of Cart 1's graph decreases by only \(2.0 \text{ m/s}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124279/*