---
title: "A block of mass \\(m\\) is initially at rest at position \\(x = 0\\) on a frictionless horizontal surface. Starting at time \\(t = 0\\), a net horizontal force with magnitude \\(F(x) = \\beta x^2\\) is applied to the block in the \\(+x\\)-direction, where \\(\\beta\\) is a positive constant. Which of the following integrals correctly represents the magnitude of the impulse delivered to the block as it travels from \\(x = 0\\) to \\(x = L\\)?"
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url: "https://nerd-notes.com/ubq/120734/"
date_modified: "2026-08-23T04:42:55+00:00"
---

# A block of mass \(m\) is initially at rest at position \(x = 0\) on a frictionless horizontal surface. Starting at time \(t = 0\), a net horizontal force with magnitude \(F(x) = \beta x^2\) is applied to the block in the \(+x\)-direction, where \(\beta\) is a positive constant. Which of the following integrals correctly represents the magnitude of the impulse delivered to the block as it travels from \(x = 0\) to \(x = L\)?

A block of mass \(m\) is initially at rest at position \(x = 0\) on a frictionless horizontal surface. Starting at time \(t = 0\), a net horizontal force with magnitude \(F(x) = \beta x^2\) is applied to the block in the \(+x\)-direction, where \(\beta\) is a positive constant. Which of the following integrals correctly represents the magnitude of the impulse delivered to the block as it travels from \(x = 0\) to \(x = L\)?

![A horizontal line represents a frictionless surface with two labeled points at \(x = 0\) and \(x = L\). A small rectangular block labeled \(m\) rests at \(x = 0\). A single horizontal arrow originating from the right side of the block points to the right along the surface toward \(x = L\) and is labeled \(F(x) = \beta x^2\). A horizontal coordinate axis beneath the surface points to the right and is labeled \(x\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460175-zoYoq7.jpg)

- **A.** \(\int_0^L \sqrt{\dfrac{m\beta x}{2}}\,dx\)
- **B.** \(\int_0^L \sqrt{\dfrac{3m\beta x}{2}}\,dx\)
- **C.** \(\int_0^L \sqrt{\dfrac{2m\beta x}{3}}\,dx\)
- **D.** \(\int_0^L \sqrt{3m\beta x}\,dx\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120734/*