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, it's dW/dt = 3.5 + 12.4tdW=3.5 + 12.4t
no, they are asking for the instantaneous power at t=3.1Le_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?
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?
which i now realize i was thinking of W/Δt.. oopsLe_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.
Instantaneous power calculation is the measurement of the rate at which energy is being transferred or used at a specific moment in time. It is typically represented by the letter P and measured in watts (W).
Instantaneous power can be calculated by dividing the change in energy by the change in time, or by multiplying the voltage and current at a specific moment in time. It can also be calculated using the formula P = VI, where V represents voltage and I represents current.
The main difference between average power and instantaneous power is the time period over which they are measured. Average power is calculated over a longer period of time, while instantaneous power is measured at a specific moment in time. Average power provides an overall picture of energy usage, while instantaneous power shows how energy is being used at a particular moment.
Instantaneous power is important in scientific research because it allows for a more detailed and accurate analysis of energy usage and transfer. It can provide insights into the performance and efficiency of systems and can help identify potential issues or improvements. It is also a crucial factor in understanding the behavior and characteristics of different materials and devices.
Instantaneous power calculation has many applications in various fields, including engineering, physics, and biology. It is commonly used in the design and analysis of electrical systems, as well as in the study of energy transfer and conversion. It is also used in research on human and animal physiology to measure the energy expended during physical activities.