---
title: "The angular velocity of an electric motor is \\(\\omega = \\left(20 – \\frac{1}{2} t^2 \\right) \\, \\text{rad/s}\\), where \\(t\\) is in seconds."
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url: "https://nerd-notes.com/ubq/39098/"
date_modified: "2025-12-14T03:42:58+00:00"
---

# The angular velocity of an electric motor is \(\omega = \left(20 – \frac{1}{2} t^2 \right) \, \text{rad/s}\), where \(t\) is in seconds.

The angular velocity of an electric motor is \(\omega = \left(20 – \frac{1}{2} t^2 \right) \, \text{rad/s}\), where \(t\) is in seconds.

**Part a)** At what time does the motor reverse direction? *(3 points)*

**Part b)** Through what angle does the motor turn between \( t = 0 \, \text{s} \) and \( t = 8 \, \text{s} \)? Hint: Use a graph if you haven’t learned calculus yet. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/39098/*