---
title: "An object moves along the \\(x\\)-axis. Its position \\(x\\) as a function of time \\(t\\) is shown in the graph and modeled by \\(x(t) = b t^2 – c t + x_0\\), where \\(b = 2.0 \\text{ m/s}^2\\), \\(c = 4.0 \\text{ m/s}\\), and \\(x_0 = 3.0 \\text{ m}\\). What is the instantaneous velocity of the object at \\(t = 3.0 \\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/117600/"
date_modified: "2026-08-04T07:49:16+00:00"
---

# An object moves along the \(x\)-axis. Its position \(x\) as a function of time \(t\) is shown in the graph and modeled by \(x(t) = b t^2 – c t + x_0\), where \(b = 2.0 \text{ m/s}^2\), \(c = 4.0 \text{ m/s}\), and \(x_0 = 3.0 \text{ m}\). What is the instantaneous velocity of the object at \(t = 3.0 \text{ s}\)?

An object moves along the \(x\)-axis. Its position \(x\) as a function of time \(t\) is shown in the graph and modeled by \(x(t) = b t^2 - c t + x_0\), where \(b = 2.0 \text{ m/s}^2\), \(c = 4.0 \text{ m/s}\), and \(x_0 = 3.0 \text{ m}\). What is the instantaneous velocity of the object at \(t = 3.0 \text{ s}\)?

![A gridless coordinate graph with a horizontal axis labeled \(t\text{ (s)}\) from 0 to 4 with tick marks at 0, 1, 2, 3, and 4, and a vertical axis labeled \(x\text{ (m)}\) from 0 to 10 with tick marks at 0, 2, 4, 6, 8, and 10. A single smooth, solid concave-up parabolic curve begins at \((0, 3.0)\), extends downward to a local minimum vertex at \((1.0, 1.0)\), and curves upward passing through \((2.0, 3.0)\) and \((3.0, 9.0)\). A filled black circle marks the point on the curve at \((3.0, 9.0)\). A short dashed tangent line segment passes through \((3.0, 9.0)\) indicating the slope at that point. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829756-U31IV9.jpg)

- **A.** \(8.0 \text{ m/s}\)
- **B.** \(12 \text{ m/s}\)
- **C.** \(16 \text{ m/s}\)
- **D.** \(18 \text{ m/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117600/*