---
title: "A motorized cart moves along a horizontal track at a constant speed \\( v \\). The motor must exert a constant forward force to overcome a constant resistive force \\( F_D \\) from the track, resulting in a power output \\( P \\). The cart then reaches a section of the track inclined at an angle \\( \\theta \\) to the horizontal and continues to move up the incline at the same constant speed \\( v \\). The magnitude of the resistive force \\( F_D \\) remains the same on the incline. On this incline, the magnitude of the component of the cart’s weight parallel to the track is equal to \\( F_D \\).   What is the new power output of the motor while the cart moves up the incline at speed \\( v \\)?"
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url: "https://nerd-notes.com/ubq/109307/"
date_modified: "2026-03-21T23:23:43+00:00"
---

# A motorized cart moves along a horizontal track at a constant speed \( v \). The motor must exert a constant forward force to overcome a constant resistive force \( F_D \) from the track, resulting in a power output \( P \). The cart then reaches a section of the track inclined at an angle \( \theta \) to the horizontal and continues to move up the incline at the same constant speed \( v \). The magnitude of the resistive force \( F_D \) remains the same on the incline. On this incline, the magnitude of the component of the cart’s weight parallel to the track is equal to \( F_D \). 

What is the new power output of the motor while the cart moves up the incline at speed \( v \)?

A motorized cart moves along a horizontal track at a constant speed \( v \). The motor must exert a constant forward force to overcome a constant resistive force \( F_D \) from the track, resulting in a power output \( P \). The cart then reaches a section of the track inclined at an angle \( \theta \) to the horizontal and continues to move up the incline at the same constant speed \( v \). The magnitude of the resistive force \( F_D \) remains the same on the incline. On this incline, the magnitude of the component of the cart's weight parallel to the track is equal to \( F_D \). 

What is the new power output of the motor while the cart moves up the incline at speed \( v \)?

![Two scenarios are shown. Scenario 1: A cart on a horizontal line moving right with velocity v. A forward force vector and a backward resistive force vector are shown with equal lengths. Scenario 2: The same cart on an incline of angle theta. It moves up the incline with velocity v. There is a forward force vector from the motor, a backward resistive force vector, and a backward weight component vector.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774135422-8O61lJ.jpg)

- **A.** \( 0.5P \)
- **B.** \( P \)
- **C.** \( 2P \)
- **D.** \( 4P \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109307/*