---
title: "An object of mass \\(m\\) is initially at rest on a horizontal, frictionless surface. At time \\(t = 0\\), a time-dependent force directed along the surface \\(F(t) = F_0 e^{-t/\\tau}\\) is applied to the object, where \\(F_0\\) and \\(\\tau\\) are positive constants. What is the maximum instantaneous power delivered to the object by this force?"
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url: "https://nerd-notes.com/ubq/117556/"
date_modified: "2026-08-04T07:49:04+00:00"
---

# An object of mass \(m\) is initially at rest on a horizontal, frictionless surface. At time \(t = 0\), a time-dependent force directed along the surface \(F(t) = F_0 e^{-t/\tau}\) is applied to the object, where \(F_0\) and \(\tau\) are positive constants. What is the maximum instantaneous power delivered to the object by this force?

An object of mass \(m\) is initially at rest on a horizontal, frictionless surface. At time \(t = 0\), a time-dependent force directed along the surface \(F(t) = F_0 e^{-t/\tau}\) is applied to the object, where \(F_0\) and \(\tau\) are positive constants. What is the maximum instantaneous power delivered to the object by this force?

- **A.** \(\dfrac{F_0^2 \tau}{4m}\)
- **B.** \(\dfrac{F_0^2 \tau}{2m}\)
- **C.** \(\dfrac{F_0^2 \tau}{e m}\)
- **D.** \(\dfrac{F_0^2 \tau}{m}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117556/*