---
title: "An object moves along the \\(x\\)-axis. Its position \\(x\\) as a function of time \\(t\\) over the interval \\(0 \\le t \\le t_3\\) is shown in the graph. The curve starts with a horizontal tangent at \\(t = 0\\), has an inflection point at \\(t = t_1\\) where the concavity changes from upward to downward, reaches a local maximum with a horizontal tangent at \\(t = t_2\\), and continues downward through \\(t_3\\).  Which of the following graphs best represents the object’s velocity \\(v\\) 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/120530/"
date_modified: "2026-08-23T04:39:31+00:00"
---

# An object moves along the \(x\)-axis. Its position \(x\) as a function of time \(t\) over the interval \(0 \le t \le t_3\) is shown in the graph. The curve starts with a horizontal tangent at \(t = 0\), has an inflection point at \(t = t_1\) where the concavity changes from upward to downward, reaches a local maximum with a horizontal tangent at \(t = t_2\), and continues downward through \(t_3\).

Which of the following graphs best represents the object’s velocity \(v\) as a function of time \(t\) over the same interval?

An object moves along the \(x\)-axis. Its position \(x\) as a function of time \(t\) over the interval \(0 \le t \le t_3\) is shown in the graph. The curve starts with a horizontal tangent at \(t = 0\), has an inflection point at \(t = t_1\) where the concavity changes from upward to downward, reaches a local maximum with a horizontal tangent at \(t = t_2\), and continues downward through \(t_3\).

Which of the following graphs best represents the object's velocity \(v\) as a function of time \(t\) over the same interval?

![A graph of position \(x\) versus time \(t\) on bare Cartesian axes. The horizontal axis is labeled \(t\) with tick marks at the origin \(0\), \(t_1\), \(t_2\), and \(t_3\) in increasing order. The vertical axis is labeled \(x\). A single solid curve begins at the origin \((0,0)\) tangent to the horizontal axis. From \(t = 0\) to \(t = t_1\), the curve rises and is concave upward. At \(t = t_1\), marked with a vertical dashed reference line to the time axis, the curve exhibits an inflection point. From \(t = t_1\) to \(t = t_2\), the curve continues rising with concave downward curvature, reaching a local maximum with a horizontal tangent at \(t = t_2\), which is marked by a vertical dashed reference line to the time axis. From \(t = t_2\) to \(t = t_3\), the curve slopes downward with continued concave downward curvature. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459970-Tva7Vm.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/120530/*