Question

what is the derivation of potential energy
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Answer 1

potential energy is denoted by letter U

Energy = Force(F)× displacement(s)

= Fs

F = mg

s can be taken as height (h)
Therefore,
U= Fs
=mgh

Answer 2

$\mathfrak{ Derivation \: of \: Potential \: Energy}$

$\mathsf{Things \: to \: know \: before\: Derivation}$

$\mathsf{\implies Work \: done = Fs = F × height = \: Fh}$

$\mathsf{\implies Work = Energy}$

$\mathsf{\implies Force = mass \: × \: acceleration \: = ma}$

$\sf{\implies Acceleration \:due \:to \:gravity =\: 'g'}$

$\mathsf{\implies Potential \: Energy \: is \: also \: written \: as \: E_p}$

$\mathsf{Derivation}$

$\mathsf{\hookrightarrow E_p = Work done = Fs = Fh }$

$\mathsf{\hookrightarrow E_p \: = \: Fh \: = ma × h }$

$\mathsf{\hookrightarrow E_p\: = \: Fh \: = mg × h }$

$\mathsf{\hookrightarrow E_p\: = \:mgh }$