---
title: "The position \\(x\\) of an object moving along the \\(x\\)-axis as a function of time \\(t\\) is modeled by \\(x(t) = x_0 \\cos(\\omega t)\\), where \\(x_0\\) is a positive constant and \\(\\omega = \\dfrac{2\\pi}{T}\\). The object’s motion over one complete period from \\(t = 0\\) to \\(t = T\\) is shown in the graph. Which of the following graphs best represents the acceleration \\(a\\) of the object as a function of time \\(t\\) over the same interval?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/124083/"
date_modified: "2026-09-28T13:30:21+00:00"
---

# The position \(x\) of an object moving along the \(x\)-axis as a function of time \(t\) is modeled by \(x(t) = x_0 \cos(\omega t)\), where \(x_0\) is a positive constant and \(\omega = \dfrac{2\pi}{T}\). The object’s motion over one complete period from \(t = 0\) to \(t = T\) is shown in the graph. Which of the following graphs best represents the acceleration \(a\) of the object as a function of time \(t\) over the same interval?

The position \(x\) of an object moving along the \(x\)-axis as a function of time \(t\) is modeled by \(x(t) = x_0 \cos(\omega t)\), where \(x_0\) is a positive constant and \(\omega = \dfrac{2\pi}{T}\). The object's motion over one complete period from \(t = 0\) to \(t = T\) is shown in the graph. Which of the following graphs best represents the acceleration \(a\) of the object as a function of time \(t\) over the same interval?

![A Cartesian graph with a horizontal time axis labeled \(t\) and a vertical position axis labeled \(x\). The horizontal axis has five tick marks labeled \(0\), \(T/4\), \(T/2\), \(3T/4\), and \(T\). The vertical axis has three tick marks labeled \(+x_0\), \(0\), and \(-x_0\). A single solid curve represents a smooth cosine wave starting at \((0, x_0)\), crossing the horizontal axis downward at \(t = T/4\), reaching a smooth minimum at \((T/2, -x_0)\), crossing the horizontal axis upward at \(t = 3T/4\), and reaching a smooth maximum at \((T, x_0)\). Dashed horizontal guide lines extend from \(+x_0\) and \(-x_0\) across the plot. No other labels, lines, text, or curves appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602220-L6uOn0.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124083/*