---
title: "An object of mass \\(m\\) is initially at rest on a frictionless horizontal surface. Beginning at time \\(t = 0\\), a net horizontal force \\(F(t) = F_0 e^{-t/\\tau}\\) acts on the object along the \\(+x\\)-direction, where \\(F_0\\) and \\(\\tau\\) are positive constants. The graph displays the net force \\(F\\) as a function of time \\(t\\). Which of the following statements correctly interprets the physical quantities represented by the graph?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120723/"
date_modified: "2026-08-23T04:42:51+00:00"
---

# An object of mass \(m\) is initially at rest on a frictionless horizontal surface. Beginning at time \(t = 0\), a net horizontal force \(F(t) = F_0 e^{-t/\tau}\) acts on the object along the \(+x\)-direction, where \(F_0\) and \(\tau\) are positive constants. The graph displays the net force \(F\) as a function of time \(t\). Which of the following statements correctly interprets the physical quantities represented by the graph?

An object of mass \(m\) is initially at rest on a frictionless horizontal surface. Beginning at time \(t = 0\), a net horizontal force \(F(t) = F_0 e^{-t/\tau}\) acts on the object along the \(+x\)-direction, where \(F_0\) and \(\tau\) are positive constants. The graph displays the net force \(F\) as a function of time \(t\). Which of the following statements correctly interprets the physical quantities represented by the graph?

![A Cartesian coordinate graph with a horizontal axis labeled t and a vertical axis labeled F. A single continuous smooth solid curve starts on the vertical axis at (0, F_0) and decays asymptotically toward the positive horizontal axis as t increases to the right. A dashed vertical line extends upward from the tick mark \tau on the horizontal axis to intersect the curve at a vertical level marked F_0/e on the vertical axis. The axes have arrowheads at their positive ends. No other curves, labels, or shaded areas appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460170-FJ5k15.jpg)

- **A.** The magnitude of the slope of the curve at any time \(t\) represents the instantaneous acceleration of the object.
- **B.** The total area bounded by the curve and the time axis as \(t \to \infty\) is finite and equal to \(F_0 \tau\), which represents the maximum momentum gained by the object.
- **C.** The total impulse delivered to the object over the time interval from \(t = 0\) to \(t = \tau\) is equal to \(\dfrac{F_0 \tau}{e}\).
- **D.** Because the force acts for an infinite duration without reaching zero at any finite time, the total area under the curve diverges, causing the object's speed to increase without bound.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120723/*