# What is the rate of change of power?

• DespicableMe
In summary, the conversation is about finding the rate of change of power produced by an engine, given a specific resistance value. The equation for power is P(R) = 130R / [(R+0.8)2], and the rate of change can be calculated using the derivative of this equation with respect to R. After some confusion and clarification, it is determined that the simplified form of the derivative is 125/R2.
DespicableMe

## Homework Statement

POwer P in watts, produced by an engine is P(R) = 130R / [(R+0.8)2 ] where R is resistance. What is the rate of change of power when R = 5?

## The Attempt at a Solution

I do not understand how the rate of change for this is

130/ ( (R+0.8)2) - 2(130R) / ((R+0.8)3)

I have tried plugging in R=5 into what I just typed above and I got the right answer. I just don't understand how they got to that equation.

One site wrote that the ROC of current with respect to resistance is 125/R2, for example, if current was 125/R

Well, what you typed there is the derivative of P(R) with respect to R. I think that's what they are asking for. What are you confused about?

Dick said:
Well, what you typed there is the derivative of P(R) with respect to R. I think that's what they are asking for. What are you confused about?

They simplified the form of the quotient rule, so I wasn't sure why the whole thing was over the denominator to the power of 3 instead of the power of 4.

When I did the quotient rule again, I understood where I went wrong and how they simplified it, so I have the answer now. Thanks.

## What is the rate of change of power?

The rate of change of power is the rate at which power, or the amount of work done per unit of time, is changing. It is a measure of how quickly power is increasing or decreasing over time.

## Why is the rate of change of power important?

The rate of change of power is important because it can help us understand the efficiency and performance of a system. It can also be used to predict future power output or identify potential issues that may arise in a system.

## How is the rate of change of power calculated?

The rate of change of power can be calculated by taking the derivative of the power function with respect to time. This can be done using calculus or by using numerical methods to approximate the derivative.

## What are some real-world examples of the rate of change of power?

Some real-world examples of the rate of change of power include the acceleration of a car or the change in power output of a wind turbine. It can also be applied to financial markets, where the rate of change of power can represent the change in value of a stock over time.

## How does the rate of change of power relate to other concepts in physics?

The rate of change of power is closely related to other concepts in physics, such as work, energy, and velocity. It is also related to the concept of force, as power is equal to the product of force and velocity. Understanding the rate of change of power can help us better understand and analyze various physical systems.

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