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title: "A test sled starts from rest at position \\(x = 0\\) at time \\(t = 0\\) and travels along a straight, horizontal track. The acceleration of the sled as a function of time is given by \\(a(t) = ct\\), where \\(c\\) is a positive constant. Position \\(x\\) and time \\(t\\) data are recorded throughout the trial. If \\(x\\) is plotted on the vertical axis, which quantity should be plotted on the horizontal axis to yield a linear graph, and how can the constant \\(c\\) be calculated from the slope \\(S\\) of the best-fit line?"
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url: "https://nerd-notes.com/ubq/123957/"
date_modified: "2026-09-28T13:27:46+00:00"
---

# A test sled starts from rest at position \(x = 0\) at time \(t = 0\) and travels along a straight, horizontal track. The acceleration of the sled as a function of time is given by \(a(t) = ct\), where \(c\) is a positive constant. Position \(x\) and time \(t\) data are recorded throughout the trial. If \(x\) is plotted on the vertical axis, which quantity should be plotted on the horizontal axis to yield a linear graph, and how can the constant \(c\) be calculated from the slope \(S\) of the best-fit line?

A test sled starts from rest at position \(x = 0\) at time \(t = 0\) and travels along a straight, horizontal track. The acceleration of the sled as a function of time is given by \(a(t) = ct\), where \(c\) is a positive constant. Position \(x\) and time \(t\) data are recorded throughout the trial. If \(x\) is plotted on the vertical axis, which quantity should be plotted on the horizontal axis to yield a linear graph, and how can the constant \(c\) be calculated from the slope \(S\) of the best-fit line?

- **A.** \(t^2\) on the horizontal axis, and \(c = 2S\)
- **B.** \(t^3\) on the horizontal axis, and \(c = 3S\)
- **C.** \(t^3\) on the horizontal axis, and \(c = 6S\)
- **D.** \(t^3\) on the horizontal axis, and \(c = \dfrac{S}{6}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123957/*