---
title: "A motor delivers mechanical power to a sled according to the function \\(P(t) = \\beta t^2\\), where \\(\\beta\\) is a positive constant and \\(t\\) is time. The sled starts from rest at \\(t = 0\\). Which of the following expressions gives the total work done by the motor on the sled from \\(t = 0\\) to \\(t = T\\)?"
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url: "https://nerd-notes.com/ubq/117533/"
date_modified: "2026-08-04T07:48:54+00:00"
---

# A motor delivers mechanical power to a sled according to the function \(P(t) = \beta t^2\), where \(\beta\) is a positive constant and \(t\) is time. The sled starts from rest at \(t = 0\). Which of the following expressions gives the total work done by the motor on the sled from \(t = 0\) to \(t = T\)?

A motor delivers mechanical power to a sled according to the function \(P(t) = \beta t^2\), where \(\beta\) is a positive constant and \(t\) is time. The sled starts from rest at \(t = 0\). Which of the following expressions gives the total work done by the motor on the sled from \(t = 0\) to \(t = T\)?

- **A.** \(2 \beta T\)
- **B.** \(\dfrac{1}{2} \beta T^3\)
- **C.** \(\dfrac{1}{3} \beta T^3\)
- **D.** \(\beta T^3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117533/*