---
title: "Two identical test carts, each of mass \\(M\\), travel horizontally at the same initial speed \\(v_0\\) across a frictionless surface toward a fixed vertical wall and come completely to rest without rebounding. Cart 1 is equipped with a rigid bumper that brings it to rest in a time interval \\(\\Delta t_1\\), whereas Cart 2 is equipped with a collapsible crumple zone that increases the stopping time interval to \\(\\Delta t_2 > \\Delta t_1\\). Which of the following statements correctly compares the average force \\(F_{\\text{avg}}\\) exerted by the wall on Cart 2 to that on Cart 1, and provides the correct justification?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120737/"
date_modified: "2026-08-23T04:42:55+00:00"
---

# Two identical test carts, each of mass \(M\), travel horizontally at the same initial speed \(v_0\) across a frictionless surface toward a fixed vertical wall and come completely to rest without rebounding. Cart 1 is equipped with a rigid bumper that brings it to rest in a time interval \(\Delta t_1\), whereas Cart 2 is equipped with a collapsible crumple zone that increases the stopping time interval to \(\Delta t_2 > \Delta t_1\). Which of the following statements correctly compares the average force \(F_{\text{avg}}\) exerted by the wall on Cart 2 to that on Cart 1, and provides the correct justification?

Two identical test carts, each of mass \(M\), travel horizontally at the same initial speed \(v_0\) across a frictionless surface toward a fixed vertical wall and come completely to rest without rebounding. Cart 1 is equipped with a rigid bumper that brings it to rest in a time interval \(\Delta t_1\), whereas Cart 2 is equipped with a collapsible crumple zone that increases the stopping time interval to \(\Delta t_2 > \Delta t_1\). Which of the following statements correctly compares the average force \(F_{\text{avg}}\) exerted by the wall on Cart 2 to that on Cart 1, and provides the correct justification?

![A grayscale schematic showing two identical rectangular carts labeled Cart 1 and Cart 2 on a flat horizontal track, moving rightward toward a fixed vertical wall with hatched shading on its right. Each cart is labeled with mass M and has an arrow pointing to the right labeled v_0 above it. Cart 1 has a thin rectangular rigid bumper attached to its right end. Cart 2 has a compressible zigzag crumple zone attached to its right end. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460175-Xc1Zhv.jpg)

- **A.** The average force on Cart 2 is less than that on Cart 1 because the total change in momentum is identical for both carts, making the average force inversely proportional to the duration of the collision.
- **B.** The average force on Cart 2 is less than that on Cart 1 because the crumple zone absorbs a portion of the cart's linear momentum during deformation, reducing the total impulse required to stop the cart.
- **C.** The average force on Cart 2 is equal to that on Cart 1 because both carts have the same initial kinetic energy and come to rest, requiring the same total energy dissipation.
- **D.** The average force on Cart 2 is greater than that on Cart 1 because the crumple zone deforms over a longer time interval, increasing the total impulse delivered to the cart.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120737/*