---
title: "A cart of mass \\(m = 2.0 \\text{ kg}\\) moves along a straight horizontal track. A sensor measures the net force \\(F(t)\\) applied to the cart during an interaction, as shown in the force-versus-time graph. The force increases quadratically from \\(t = 0 \\text{ s}\\) to \\(t = 3.0 \\text{ s}\\) according to \\(F(t) = c t^2\\), reaching a maximum value of \\(18 \\text{ N}\\) at \\(t = 3.0 \\text{ s}\\), after which the force drops instantly to zero. What is the average force \\(F_{\\text{avg}}\\) exerted on the cart during the time interval from \\(t = 0 \\text{ s}\\) to \\(t = 3.0 \\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/117613/"
date_modified: "2026-08-04T07:49:19+00:00"
---

# A cart of mass \(m = 2.0 \text{ kg}\) moves along a straight horizontal track. A sensor measures the net force \(F(t)\) applied to the cart during an interaction, as shown in the force-versus-time graph. The force increases quadratically from \(t = 0 \text{ s}\) to \(t = 3.0 \text{ s}\) according to \(F(t) = c t^2\), reaching a maximum value of \(18 \text{ N}\) at \(t = 3.0 \text{ s}\), after which the force drops instantly to zero. What is the average force \(F_{\text{avg}}\) exerted on the cart during the time interval from \(t = 0 \text{ s}\) to \(t = 3.0 \text{ s}\)?

A cart of mass \(m = 2.0 \text{ kg}\) moves along a straight horizontal track. A sensor measures the net force \(F(t)\) applied to the cart during an interaction, as shown in the force-versus-time graph. The force increases quadratically from \(t = 0 \text{ s}\) to \(t = 3.0 \text{ s}\) according to \(F(t) = c t^2\), reaching a maximum value of \(18 \text{ N}\) at \(t = 3.0 \text{ s}\), after which the force drops instantly to zero. What is the average force \(F_{\text{avg}}\) exerted on the cart during the time interval from \(t = 0 \text{ s}\) to \(t = 3.0 \text{ s}\)?

![A 2D line graph of force F in newtons versus time t in seconds. The horizontal axis is labeled t (s) with tick marks at 0, 1.0, 2.0, and 3.0. The vertical axis is labeled F (N) with tick marks at 0, 6, 12, and 18. A curve starts at the origin (0, 0) and curves upward quadratically (concave up) to a peak point at (3.0, 18). At t = 3.0 s, a vertical dashed line drops down from (3.0, 18) to (3.0, 0) on the horizontal axis. A dashed horizontal reference line extends from (0, 18) to (3.0, 18). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829759-IST48J.jpg)

- **A.** \(6.0 \text{ N}\)
- **B.** \(9.0 \text{ N}\)
- **C.** \(12 \text{ N}\)
- **D.** \(18 \text{ N}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117613/*