---
title: "A motorized winch lifts a crate vertically from rest. The power \\(P\\) delivered by the winch as a function of time \\(t\\) increases linearly from \\(0\\text{ W}\\) at \\(t = 0\\text{ s}\\) to \\(120\\text{ W}\\) at \\(t = 4\\text{ s}\\), remains constant at \\(120\\text{ W}\\) until \\(t = 8\\text{ s}\\), and then decreases linearly to \\(0\\text{ W}\\) at \\(t = 10\\text{ s}\\), as shown in the graph. Which of the following statements correctly interprets the work done or power delivered during this process?"
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url: "https://nerd-notes.com/ubq/124025/"
date_modified: "2026-09-28T13:30:13+00:00"
---

# A motorized winch lifts a crate vertically from rest. The power \(P\) delivered by the winch as a function of time \(t\) increases linearly from \(0\text{ W}\) at \(t = 0\text{ s}\) to \(120\text{ W}\) at \(t = 4\text{ s}\), remains constant at \(120\text{ W}\) until \(t = 8\text{ s}\), and then decreases linearly to \(0\text{ W}\) at \(t = 10\text{ s}\), as shown in the graph. Which of the following statements correctly interprets the work done or power delivered during this process?

A motorized winch lifts a crate vertically from rest. The power \(P\) delivered by the winch as a function of time \(t\) increases linearly from \(0\text{ W}\) at \(t = 0\text{ s}\) to \(120\text{ W}\) at \(t = 4\text{ s}\), remains constant at \(120\text{ W}\) until \(t = 8\text{ s}\), and then decreases linearly to \(0\text{ W}\) at \(t = 10\text{ s}\), as shown in the graph. Which of the following statements correctly interprets the work done or power delivered during this process?

![A Cartesian coordinate graph showing power versus time. The horizontal axis is labeled \(t\text{ (s)}\) with numerical tick marks at 0, 2, 4, 6, 8, and 10. The vertical axis is labeled \(P\text{ (W)}\) with numerical tick marks at 0, 40, 80, and 120. Thin, dashed gray gridlines extend across the plot at each major tick mark. A single thick, solid black line represents the piecewise linear function: starting at the origin (0, 0), it extends upward to the point (4, 120), continues horizontally to the point (8, 120), and then slopes downward to end at (10, 0) on the horizontal axis. No other curves, labels, shading, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602213-CGKoWp.jpg)

- **A.** The average power delivered over the \(10\text{ s}\) interval is \(84\text{ W}\), because the total work done is the time integral of power, which equals the area under the curve divided by the total time.
- **B.** The average power delivered over the \(10\text{ s}\) interval is \(60\text{ W}\), because the average power is the arithmetic mean of the minimum and maximum power values.
- **C.** No energy is transferred to the crate at \(t = 4\text{ s}\), because the slope of the curve is zero at this point.
- **D.** Negative work is done on the crate from \(t = 8\text{ s}\) to \(t = 10\text{ s}\), because the slope of the curve is negative during this interval.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124025/*