---
title: "A block of mass \\(m\\) moves along the \\(x\\)-axis on a frictionless horizontal surface. At position \\(x = 0\\), the block has a speed \\(v_0\\) in the \\(+x\\)-direction. A net horizontal force directed along the \\(x\\)-axis is applied to the block, given by \\(F(x) = \\alpha x^2\\), where \\(\\alpha\\) is a positive constant. Which of the following expressions represents the speed of the block when it reaches position \\(x = L\\)?"
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url: "https://nerd-notes.com/ubq/120638/"
date_modified: "2026-08-23T04:42:26+00:00"
---

# A block of mass \(m\) moves along the \(x\)-axis on a frictionless horizontal surface. At position \(x = 0\), the block has a speed \(v_0\) in the \(+x\)-direction. A net horizontal force directed along the \(x\)-axis is applied to the block, given by \(F(x) = \alpha x^2\), where \(\alpha\) is a positive constant. Which of the following expressions represents the speed of the block when it reaches position \(x = L\)?

A block of mass \(m\) moves along the \(x\)-axis on a frictionless horizontal surface. At position \(x = 0\), the block has a speed \(v_0\) in the \(+x\)-direction. A net horizontal force directed along the \(x\)-axis is applied to the block, given by \(F(x) = \alpha x^2\), where \(\alpha\) is a positive constant. Which of the following expressions represents the speed of the block when it reaches position \(x = L\)?

![A horizontal surface with a horizontal coordinate line labeled x. A rectangular block of mass m is shown at position x = 0. A horizontal rightward arrow above the block is labeled v_0. A horizontal rightward force arrow acting on the block is labeled F(x) = \alpha x^2. A dashed vertical tick mark on the x-axis to the right of the block is labeled x = L. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460146-hJvfYD.jpg)

- **A.** \(\sqrt{v_0^2 + \dfrac{\alpha L^3}{3m}}\)
- **B.** \(\sqrt{v_0^2 + \dfrac{2\alpha L^3}{3m}}\)
- **C.** \(\sqrt{v_0^2 + \dfrac{\alpha L^3}{m}}\)
- **D.** \(\sqrt{v_0^2 + \dfrac{2\alpha L^3}{m}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120638/*