# Instantaneous Power calculation

1. Apr 7, 2016

### Le_Anthony

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
P=dW/dt
J/s=watt

3. 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???

2. Apr 7, 2016

No.

3. Apr 7, 2016

### Staff: Mentor

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

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

4. Apr 7, 2016

### donpacino

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?

5. Apr 7, 2016

### Le_Anthony

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.

6. Apr 7, 2016

### Le_Anthony

which i now realize i was thinking of W/Δt.. oops