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title: "An object of mass \\(2.0 \\text{ kg}\\) moves along the \\(x\\)-axis with an initial velocity of \\(-3.0 \\text{ m/s}\\) at time \\(t = 0\\). The object is acted upon by a net force \\(F_x(t)\\) directed along the \\(x\\)-axis, as shown in the graph. The force is described by the quadratic function \\(F_x(t) = 12t – 3t^2\\) for \\(0 \\le t \\le 4.0 \\text{ s}\\), and decreases linearly from \\(0 \\text{ N}\\) at \\(t = 4.0 \\text{ s}\\) to \\(-12 \\text{ N}\\) at \\(t = 6.0 \\text{ s}\\). What is the magnitude of the linear momentum of the object at \\(t = 6.0 \\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/120773/"
date_modified: "2026-08-23T04:43:13+00:00"
---

# An object of mass \(2.0 \text{ kg}\) moves along the \(x\)-axis with an initial velocity of \(-3.0 \text{ m/s}\) at time \(t = 0\). The object is acted upon by a net force \(F_x(t)\) directed along the \(x\)-axis, as shown in the graph. The force is described by the quadratic function \(F_x(t) = 12t – 3t^2\) for \(0 \le t \le 4.0 \text{ s}\), and decreases linearly from \(0 \text{ N}\) at \(t = 4.0 \text{ s}\) to \(-12 \text{ N}\) at \(t = 6.0 \text{ s}\). What is the magnitude of the linear momentum of the object at \(t = 6.0 \text{ s}\)?

An object of mass \(2.0 \text{ kg}\) moves along the \(x\)-axis with an initial velocity of \(-3.0 \text{ m/s}\) at time \(t = 0\). The object is acted upon by a net force \(F_x(t)\) directed along the \(x\)-axis, as shown in the graph. The force is described by the quadratic function \(F_x(t) = 12t - 3t^2\) for \(0 \le t \le 4.0 \text{ s}\), and decreases linearly from \(0 \text{ N}\) at \(t = 4.0 \text{ s}\) to \(-12 \text{ N}\) at \(t = 6.0 \text{ s}\). What is the magnitude of the linear momentum of the object at \(t = 6.0 \text{ s}\)?

![A 2D line graph with a horizontal axis labeled \(t\text{ (s)}\) and a vertical axis labeled \(F_x\text{ (N)}\). The horizontal axis has tick marks and numerical labels at 0, 1, 2, 3, 4, 5, and 6. The vertical axis extends from -15 to 15 with tick marks and numerical labels at -12, -6, 0, 6, and 12. Light gray gridlines align with each integer tick mark on both axes. A single continuous solid black curve depicts the force. Starting at the origin (0, 0), the curve arches smoothly upward in a concave-down parabolic shape to a peak at (2, 12), then curves downward to intersect the horizontal axis at (4, 0). From (4, 0), the curve continues as a straight solid line segment sloping downward to the point (6, -12). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460192-dnAUeD.jpg)

- **A.** \(6.0 \text{ kg}\cdot\text{m/s}\)
- **B.** \(10 \text{ kg}\cdot\text{m/s}\)
- **C.** \(14 \text{ kg}\cdot\text{m/s}\)
- **D.** \(20 \text{ kg}\cdot\text{m/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120773/*