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title: "An object moves along the positive \\(x\\)-axis from \\(x = 0\\) to \\(x = L\\). Its velocity \\(v\\) as a function of position is given by \\(v(x) = v_0\\left(1 – \\dfrac{x}{L}\\right)\\), where \\(v_0\\) is a positive constant. Which of the following best describes the graph of the object’s acceleration \\(a\\) as a function of position \\(x\\) over the interval \\(0 \\le x \\le L\\)?"
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url: "https://nerd-notes.com/ubq/120476/"
date_modified: "2026-08-23T04:39:03+00:00"
---

# An object moves along the positive \(x\)-axis from \(x = 0\) to \(x = L\). Its velocity \(v\) as a function of position is given by \(v(x) = v_0\left(1 – \dfrac{x}{L}\right)\), where \(v_0\) is a positive constant. Which of the following best describes the graph of the object’s acceleration \(a\) as a function of position \(x\) over the interval \(0 \le x \le L\)?

An object moves along the positive \(x\)-axis from \(x = 0\) to \(x = L\). Its velocity \(v\) as a function of position is given by \(v(x) = v_0\left(1 - \dfrac{x}{L}\right)\), where \(v_0\) is a positive constant. Which of the following best describes the graph of the object's acceleration \(a\) as a function of position \(x\) over the interval \(0 \le x \le L\)?

- **A.** A horizontal line with a constant negative value of acceleration from \(x = 0\) to \(x = L\)
- **B.** A straight line with a positive slope, beginning at a negative value at \(x = 0\) and increasing to zero at \(x = L\)
- **C.** A straight line with a negative slope, beginning at a negative value at \(x = 0\) and decreasing to a more negative value at \(x = L\)
- **D.** A parabolic curve opening upward, beginning at a positive value at \(x = 0\) and decreasing to zero at \(x = L\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120476/*