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title: "A particle of mass \\(m\\) is initially at rest on a frictionless horizontal surface. Starting at time \\(t = 0\\), a horizontal force directed along the positive \\(x\\)-axis is applied to the particle with a time-dependent magnitude given by \\(F(t) = F_0 \\sin(\\omega t)\\), where \\(F_0\\) and \\(\\omega\\) are positive constants. The force acts until \\(t = \\dfrac{\\pi}{\\omega}\\), at which point it drops to zero. Which of the following expressions represents the speed of the particle at time \\(t = \\dfrac{\\pi}{\\omega}\\)?"
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url: "https://nerd-notes.com/ubq/123968/"
date_modified: "2026-09-28T13:29:41+00:00"
---

# A particle of mass \(m\) is initially at rest on a frictionless horizontal surface. Starting at time \(t = 0\), a horizontal force directed along the positive \(x\)-axis is applied to the particle with a time-dependent magnitude given by \(F(t) = F_0 \sin(\omega t)\), where \(F_0\) and \(\omega\) are positive constants. The force acts until \(t = \dfrac{\pi}{\omega}\), at which point it drops to zero. Which of the following expressions represents the speed of the particle at time \(t = \dfrac{\pi}{\omega}\)?

A particle of mass \(m\) is initially at rest on a frictionless horizontal surface. Starting at time \(t = 0\), a horizontal force directed along the positive \(x\)-axis is applied to the particle with a time-dependent magnitude given by \(F(t) = F_0 \sin(\omega t)\), where \(F_0\) and \(\omega\) are positive constants. The force acts until \(t = \dfrac{\pi}{\omega}\), at which point it drops to zero. Which of the following expressions represents the speed of the particle at time \(t = \dfrac{\pi}{\omega}\)?

- **A.** \(\dfrac{2 F_0}{m \omega}\)
- **B.** \(\dfrac{F_0}{m \omega}\)
- **C.** \(\dfrac{\pi F_0}{2 m \omega}\)
- **D.** \(\dfrac{\pi F_0}{m \omega}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123968/*