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Perhaps it's nice to add that in real life the concept of 'force' is much more vivid. Force has something to do with to the change in energyAvalon_18 said:I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.
Some force fields are conservative, hence the introduction of a potential (energy) with somehing like ##\Delta {\rm PE} = \vec F \cdot \Delta \vec x\ ##.
From $$ \vec F = {\Delta\vec p\over \Delta t} \Rightarrow \quad \vec F \cdot \Delta \vec x= m{\Delta\vec v\over \Delta t} \cdot \Delta\vec x = m\;\Delta\vec v \cdot {\Delta\vec x\over \Delta t} = m\;\Delta\vec v \cdot \vec v = \Delta \left ( {1\over 2 }m \vec v^2 \right ) $$ comes the formula for kinetic energy.
It's all differentiation and integration -- which makes math so useful !
[edit] hehe if you do it right
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