Instantaneous Power calculation

AI Thread Summary
The discussion focuses on calculating instantaneous power from the energy increase rate of a system given by the equation 3.5t + 6.2t^2. The correct approach involves finding the derivative of the energy function with respect to time, leading to P = 3.5 + 12.4t. Participants clarify that instantaneous power should not be divided by time, as it is a direct derivative rather than an average over a time interval. The confusion arises from misinterpreting the relationship between work and time, emphasizing the need to derive the equation before substituting the time value. Ultimately, the correct method is to derive the energy equation and evaluate it at t=3.1 seconds.
Le_Anthony
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Homework Statement


The energy of a system increases at a rate of 3.5t + 6.2t^2, in joules.
What is the instantaneous power at t=3.1 s?

Homework Equations


P=dW/dt
J/s=watt

The Attempt at a Solution


dW=3.5 + 12.4t
P=(3.5 + 12.4t joule) / (3.1s)=1.12 + 4t, in watts

Yes/ no?
 
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Le_Anthony said:

Homework Statement


The energy of a system increases at a rate of 3.5t + 6.2t^2, in joules.
What is the instantaneous power at t=3.1 s?

Homework Equations


P=dW/dt
J/s=watt

The Attempt at a Solution


dW=3.5 + 12.4t
P=(3.5 + 12.4t joule) / (3.1s)=1.12 + 4t, in watts

Yes/ no?

No.
 
dW=3.5 + 12.4t
No, it's dW/dt = 3.5 + 12.4t

Why did you divide by 3.1? What units would your answer have?
 
Le_Anthony said:

Homework Statement


The energy of a system increases at a rate of 3.5t + 6.2t^2, in joules.
What is the instantaneous power at t=3.1 s?

Homework Equations


P=dW/dt
J/s=watt

The Attempt at a Solution


dW=3.5 + 12.4t
P=(3.5 + 12.4t joule) / (3.1s)=1.12 + 4t, in watts

Yes/ no?
no, they are asking for the instantaneous power at t=3.1

why would the power at 3.1 secs be dependent on time?

1 watt does equal 1 joule per second.

I'll give you a few hints.
The average power dissipated during a time period is energy/ the time period. What happens when you decrease that time period to a very small value?

another hint. To find energy simply sum (integrate) the power. how do you go the other way?
 
donpacino said:
no, they are asking for the instantaneous power at t=3.1

why would the power at 3.1 secs be dependent on time?

1 watt does equal 1 joule per second.

I'll give you a few hints.
The average power dissipated during a time period is energy/ the time period. What happens when you decrease that time period to a very small value?

another hint. To find energy simply sum (integrate) the power. how do you go the other way?

So i just need to derive the equation and plug in 3.1s?
I divided by 3.1 because instantaneous power is derivative of work w/ respect to time.
 
Le_Anthony said:
So i just need to derive the equation and plug in 3.1s?
I divided by 3.1 because instantaneous power is derivative of work w/ respect to time.
which i now realize i was thinking of W/Δt.. oops
 

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