---
title: "Cart 1 of mass \\(m\\) and Cart 2 of mass \\(2m\\) travel along a horizontal, frictionless surface and collide. A sensor records the horizontal contact force \\(F_x\\) exerted on each cart as a function of time \\(t\\) during the collision interval from \\(t = 0\\) to \\(t = T\\). The graph displays two symmetric force curves: the force on Cart 1 reaches a maximum of \\(+F_{\\max}\\), while the force on Cart 2 reaches a minimum of \\(-F_{\\max}\\), with the two curves having identical shapes reflected across the time axis. Which of the following statements correctly interprets the collision data shown in the graph?"
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url: "https://nerd-notes.com/ubq/124313/"
date_modified: "2026-09-28T14:04:45+00:00"
---

# Cart 1 of mass \(m\) and Cart 2 of mass \(2m\) travel along a horizontal, frictionless surface and collide. A sensor records the horizontal contact force \(F_x\) exerted on each cart as a function of time \(t\) during the collision interval from \(t = 0\) to \(t = T\). The graph displays two symmetric force curves: the force on Cart 1 reaches a maximum of \(+F_{\max}\), while the force on Cart 2 reaches a minimum of \(-F_{\max}\), with the two curves having identical shapes reflected across the time axis. Which of the following statements correctly interprets the collision data shown in the graph?

Cart 1 of mass \(m\) and Cart 2 of mass \(2m\) travel along a horizontal, frictionless surface and collide. A sensor records the horizontal contact force \(F_x\) exerted on each cart as a function of time \(t\) during the collision interval from \(t = 0\) to \(t = T\). The graph displays two symmetric force curves: the force on Cart 1 reaches a maximum of \(+F_{\max}\), while the force on Cart 2 reaches a minimum of \(-F_{\max}\), with the two curves having identical shapes reflected across the time axis. Which of the following statements correctly interprets the collision data shown in the graph?

![A graph of horizontal contact force \(F_x\) on the vertical axis versus time \(t\) on the horizontal axis on bare axes with no gridlines. The horizontal axis has tick marks at \(0\), \(t_0\), and \(T\). The vertical axis has a central origin at \(0\), a positive tick mark labeled \(+F_{\max}\), and a negative tick mark labeled \(-F_{\max}\). A horizontal axis line runs at \(F_x = 0\). From \(t = 0\) to \(t = T\), a solid curve starts at \((0, 0)\), curves upward to a smooth peak at \((t_0, +F_{\max})\), and returns to \((T, 0)\), labeled Cart 1. A dashed curve starts at \((0, 0)\), curves downward to a smooth trough at \((t_0, -F_{\max})\), and returns to \((T, 0)\), labeled Cart 2. The two curves are symmetric reflections of each other across the horizontal axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604285-rzerXU.jpg)

- **A.** The curves reach the same peak magnitude \(F_{\max}\), indicating that both carts experience the same maximum acceleration during the collision.
- **B.** The bounded area between each curve and the time axis has the same magnitude, indicating that Cart 1 experiences twice the magnitude of velocity change as Cart 2.
- **C.** The bounded area between each curve and the time axis has the same magnitude, indicating that both carts experience the same magnitude of velocity change.
- **D.** The slope of each curve is zero at the peak force magnitude, indicating that the acceleration of each cart is momentarily zero at that instant.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124313/*