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I'm not sure I follow; power and energy have nothing to do with velocity or acceleration in this context, its just meant to be an analogy.
If you flick a dimmer fast enough, it might distort, yes? But its unfortunately more complicated than "range of change of power" and has to do with how modern dimmers works.
Not exactly.
Where you are is your position.
The rate you get there is speed.
If you speed up or slow down, that's acceleration.
And how "smooth" your acceleration is is what we call "jerk." Slamming on gas or brakes would be a high jerk value, gradually pushing the petal until its all the way down would be a low jerk value.
Not sure I follow this, sorry. But if you're talking about overloading electrical components, unfortunately this is really complicated and gets into how AC circuits work.
And as another random suggestion, you may want to look up dimensional analysis. If you're trying to wrap your head around how stuff is represented, that's it.
For example:
We measure position in meters (m).
We measure speed in meters per second. meters / seconds, or m/s.
Acceleration is meters per second, per second. meters / (second * second), or m / s^2.
Hence jerk is m / s^3
Energy is trickier to wrap your head around.
"Force," aka how hard you push on something, can be measured as the acceleration of mass. Its unit is kilogram * meter / seconds ^2, or kg * m / s^2
Energy is force * distance. So kg * m^2 / s^2.
Power is energy per second. So kg * m^2 / s^3.
And what you were initially describing seems to be kg * m^2 / s^4.
Here's another way to look at it.
What happens if you divide power by velocity? In other words, how "fast" is the power moving?
Well, that'd be:
(kg * m^2 / s^3) divided by (m/s)
And what do you get? kg * m / s^2. That's force!
So maybe "force" is the answer to your original question of "what's the 'speed' of power moving through stuff called," if I'm interpreting it right.
I mean in this in the utmost respect but I am bookmarking this for an example of how to have a general great discourse where you battle each other with knowledge. And it only ends when one is educated more. But with all respect to you,,,you gave me a knowledge boner from the knowledge nuke you just dropped more could learn from your about engagement and discourse.