---
title: "A cart is released from rest at the top of a smooth inclined plane. A motion sensor tracks the cart’s position \\(x\\) relative to its starting point as a function of time \\(t\\). A student wants to test the hypothesis that the cart moves with a constant acceleration \\(a\\). If the student plots the position \\(x\\) on the vertical axis, what should be plotted on the horizontal axis to produce a linear graph, and what does the slope of that line represent?"
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url: "https://nerd-notes.com/ubq/109236/"
date_modified: "2026-03-21T18:07:16+00:00"
---

# A cart is released from rest at the top of a smooth inclined plane. A motion sensor tracks the cart’s position \(x\) relative to its starting point as a function of time \(t\). A student wants to test the hypothesis that the cart moves with a constant acceleration \(a\). If the student plots the position \(x\) on the vertical axis, what should be plotted on the horizontal axis to produce a linear graph, and what does the slope of that line represent?

A cart is released from rest at the top of a smooth inclined plane. A motion sensor tracks the cart's position \(x\) relative to its starting point as a function of time \(t\). A student wants to test the hypothesis that the cart moves with a constant acceleration \(a\). If the student plots the position \(x\) on the vertical axis, what should be plotted on the horizontal axis to produce a linear graph, and what does the slope of that line represent?

![A cart sits on a ramp inclined at an angle. A motion sensor is placed at the top of the ramp, pointing down toward the cart. The cart starts at x = 0 at time t = 0.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774116435-me8sRM.jpg)

- **A.** Time \(t\); slope represents the acceleration \(a\)
- **B.** Time \(t\); slope represents the average velocity of the cart
- **C.** The square of time \(t^2\); slope represents the acceleration \(a\)
- **D.** The square of time \(t^2\); slope represents half of the acceleration, \(\dfrac{1}{2}a\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109236/*