---
title: "A student conducts an experiment to determine the constant acceleration \\(a\\) of a cart that starts from rest and rolls down a long, straight incline. Using a motion sensor, the student records the cart’s position \\(x\\) at several different times \\(t\\). The cart is at position \\(x = 0\\) at time \\(t = 0\\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes respectively, will produce a linear graph that can be used to determine the acceleration of the cart?"
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url: "https://nerd-notes.com/ubq/112610/"
date_modified: "2026-04-29T21:42:25+00:00"
---

# A student conducts an experiment to determine the constant acceleration \(a\) of a cart that starts from rest and rolls down a long, straight incline. Using a motion sensor, the student records the cart’s position \(x\) at several different times \(t\). The cart is at position \(x = 0\) at time \(t = 0\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes respectively, will produce a linear graph that can be used to determine the acceleration of the cart?

A student conducts an experiment to determine the constant acceleration \(a\) of a cart that starts from rest and rolls down a long, straight incline. Using a motion sensor, the student records the cart's position \(x\) at several different times \(t\). The cart is at position \(x = 0\) at time \(t = 0\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes respectively, will produce a linear graph that can be used to determine the acceleration of the cart?

![A diagram showing a cart on a straight ramp inclined at an angle. A motion sensor is positioned at the top of the ramp, labeled x = 0. An arrow points down the ramp indicating the positive x direction. The cart is shown at a generic position x along the ramp.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777498944-pzZYGf.jpg)

- **A.** Position \(x\) and time \(t\)
- **B.** Position \(x\) and the square of time \(t^2\)
- **C.** The square of position \(x^2\) and time \(t\)
- **D.** The square root of position \(\sqrt{x}\) and the square of time \(t^2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/112610/*