---
title: "An object moves along the continuous, straight line of the x-axis. The acceleration \\(a\\) of the object as a function of time \\(t\\) increases linearly from \\(a(0) = 2.0 \\text{ m/s}^2\\) at \\(t = 0 \\text{ s}\\) to \\(a(4.0) = 14.0 \\text{ m/s}^2\\) at \\(t = 4.0 \\text{ s}\\), as depicted in the graph. What is the change in the velocity of the object, \\(\\Delta v\\), between \\(t = 0 \\text{ s}\\) and \\(t = 4.0 \\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/117587/"
date_modified: "2026-08-04T07:49:13+00:00"
---

# An object moves along the continuous, straight line of the x-axis. The acceleration \(a\) of the object as a function of time \(t\) increases linearly from \(a(0) = 2.0 \text{ m/s}^2\) at \(t = 0 \text{ s}\) to \(a(4.0) = 14.0 \text{ m/s}^2\) at \(t = 4.0 \text{ s}\), as depicted in the graph. What is the change in the velocity of the object, \(\Delta v\), between \(t = 0 \text{ s}\) and \(t = 4.0 \text{ s}\)?

An object moves along the continuous, straight line of the x-axis. The acceleration \(a\) of the object as a function of time \(t\) increases linearly from \(a(0) = 2.0 \text{ m/s}^2\) at \(t = 0 \text{ s}\) to \(a(4.0) = 14.0 \text{ m/s}^2\) at \(t = 4.0 \text{ s}\), as depicted in the graph. What is the change in the velocity of the object, \(\Delta v\), between \(t = 0 \text{ s}\) and \(t = 4.0 \text{ s}\)?

![A 2D Cartesian graph with horizontal axis labeled t (s) ranging from 0 to 5 in increments of 1, and vertical axis labeled a (m/s^2) ranging from 0 to 16 in increments of 2. Grid lines extend across the plot region. A single solid dark line begins at the point (0, 2) on the vertical axis and extends upward to the right with a constant positive slope, terminating at the point (4, 14). A filled black dot is plotted at (0, 2) and another filled black dot is plotted at (4, 14). Dashed horizontal and vertical reference lines extend from (4, 14) to the axes at t = 4 and a = 14. The area under the line between t = 0 and t = 4 is shaded light gray. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829753-PSlpBK.jpg)

- **A.** \(32 \text{ m/s}\)
- **B.** \(48 \text{ m/s}\)
- **C.** \(56 \text{ m/s}\)
- **D.** \(64 \text{ m/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117587/*