---
title: "A cart moves along a straight, level track with constant non-zero acceleration \\(a\\). A motion detector records the position \\(x\\) of the cart as a function of time \\(t\\), starting from \\(x = 0\\) at \\(t = 0\\) with an unknown initial velocity \\(v_0 \\neq 0\\). To determine \\(a\\) from a linear fit of the data, which quantities should be plotted on the vertical and horizontal axes, and what is the relationship between \\(a\\) and the slope of the resulting line?"
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url: "https://nerd-notes.com/ubq/120467/"
date_modified: "2026-08-23T04:38:56+00:00"
---

# A cart moves along a straight, level track with constant non-zero acceleration \(a\). A motion detector records the position \(x\) of the cart as a function of time \(t\), starting from \(x = 0\) at \(t = 0\) with an unknown initial velocity \(v_0 \neq 0\). To determine \(a\) from a linear fit of the data, which quantities should be plotted on the vertical and horizontal axes, and what is the relationship between \(a\) and the slope of the resulting line?

A cart moves along a straight, level track with constant non-zero acceleration \(a\). A motion detector records the position \(x\) of the cart as a function of time \(t\), starting from \(x = 0\) at \(t = 0\) with an unknown initial velocity \(v_0 \neq 0\). To determine \(a\) from a linear fit of the data, which quantities should be plotted on the vertical and horizontal axes, and what is the relationship between \(a\) and the slope of the resulting line?

- **A.** Plot \(x\) on the vertical axis and \(t^2\) on the horizontal axis; the acceleration is equal to the slope.
- **B.** Plot \(x\) on the vertical axis and \(t^2\) on the horizontal axis; the acceleration is equal to twice the slope.
- **C.** Plot \(\dfrac{x}{t}\) on the vertical axis and \(t\) on the horizontal axis; the acceleration is equal to twice the slope.
- **D.** Plot \(\dfrac{x}{t}\) on the vertical axis and \(t\) on the horizontal axis; the acceleration is equal to the slope.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120467/*