---
title: "A cart constrained to move along a straight, horizontal one-dimensional track starts from rest at the origin (x = 0\\) at \\(t = 0\\)). The cart experiences a time-dependent acceleration \\(a(t)\\) as shown in the graph from \\(t = 0\\) to \\(t = 2T\\). Which of the following graphs best represents the position \\(x\\) of the cart as a function of time \\(t\\) over the interval \\(0 \\le t \\le 2T\\)?"
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url: "https://nerd-notes.com/ubq/120536/"
date_modified: "2026-08-23T04:39:45+00:00"
---

# A cart constrained to move along a straight, horizontal one-dimensional track starts from rest at the origin (x = 0\) at \(t = 0\)). The cart experiences a time-dependent acceleration \(a(t)\) as shown in the graph from \(t = 0\) to \(t = 2T\). Which of the following graphs best represents the position \(x\) of the cart as a function of time \(t\) over the interval \(0 \le t \le 2T\)?

A cart constrained to move along a straight, horizontal one-dimensional track starts from rest at the origin (x = 0\) at \(t = 0\)). The cart experiences a time-dependent acceleration \(a(t)\) as shown in the graph from \(t = 0\) to \(t = 2T\). Which of the following graphs best represents the position \(x\) of the cart as a function of time \(t\) over the interval \(0 \le t \le 2T\)?

![A Cartesian coordinate graph showing acceleration a on the vertical axis versus time t on the horizontal axis. The horizontal axis has tick marks labeled 0, T, and 2T. The vertical axis has tick marks labeled -a_0, 0, and a_0. A single solid straight line begins at the vertical axis intercept (0, a_0), passes through the horizontal axis at (T, 0), and terminates at the point (2T, -a_0). No other lines, gridlines, text, or curves appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459984-Tg3OSI.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/120536/*