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title: "A small sphere of mass \\(m\\) is released from rest at \\(t = 0\\) at the surface of a deep column of viscous fluid. The fluid exerts a resistive drag force on the sphere given by \\(\\vec{F}_d = -b\\vec{v}\\), where \\(b\\) is a positive constant and \\(\\vec{v}\\) is the sphere’s velocity. Let the downward direction be defined as positive, with the sphere’s release position at \\(y = 0\\). Which of the following best describes the shape of the graph of the sphere’s downward acceleration \\(a\\) as a function of its downward position \\(y\\)?"
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url: "https://nerd-notes.com/ubq/123994/"
date_modified: "2026-09-28T13:30:04+00:00"
---

# A small sphere of mass \(m\) is released from rest at \(t = 0\) at the surface of a deep column of viscous fluid. The fluid exerts a resistive drag force on the sphere given by \(\vec{F}_d = -b\vec{v}\), where \(b\) is a positive constant and \(\vec{v}\) is the sphere’s velocity. Let the downward direction be defined as positive, with the sphere’s release position at \(y = 0\). Which of the following best describes the shape of the graph of the sphere’s downward acceleration \(a\) as a function of its downward position \(y\)?

A small sphere of mass \(m\) is released from rest at \(t = 0\) at the surface of a deep column of viscous fluid. The fluid exerts a resistive drag force on the sphere given by \(\vec{F}_d = -b\vec{v}\), where \(b\) is a positive constant and \(\vec{v}\) is the sphere's velocity. Let the downward direction be defined as positive, with the sphere's release position at \(y = 0\). Which of the following best describes the shape of the graph of the sphere's downward acceleration \(a\) as a function of its downward position \(y\)?

- **A.** A line with a constant negative slope that starts at \(a = g\) and intercepts the horizontal axis at a finite value of \(y\)
- **B.** A curve that starts at \(a = g\) with an infinite negative slope, is concave upward, and asymptotically approaches \(a = 0\) as \(y \to \infty\)
- **C.** A curve that starts at \(a = g\) with a slope of zero, is concave downward, and asymptotically approaches \(a = 0\) as \(y \to \infty\)
- **D.** A curve that starts at \(a = g\) with a finite negative slope, is concave upward, and asymptotically approaches \(a = 0\) as \(y \to \infty\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123994/*