Question

what is formula of kinitic energy with derivation?

Answer 1

HELLO MATE


HERE IS YOUR ANSWER


K.E. = 1/2 mv2.


It is the formula of kinetic energy with derivation.

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Answer 2

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$\orange{Bonjour!!}$

$\textbf{Derivation:}$

$\green{Expression \: For\:Kinetic\:Energy:}$

Let

$\textbf{m}$=mass of the body

$\textbf{u}$=0=¡nitial velocity of the body

$\textbf{F}$=Constant force applied on the body

$\textbf{a}$=acceleration produced in the body in the direction of force

$\textbf{v}$=final velocity of the body

$\textbf{s}$=distance covered by the body

As..

${v}^{2} - {u}^{2} = 2as \\ \\ {v}^{2} - {0}^{2} = 2as \\ \\ or \\ \\ a = \frac{ {v}^{2} }{2s }$
As the force and displacement are in same direction,so the work done is

$w = fs = ma.s = m. \frac{ {v}^{2} }{2s} .s = \frac{1}{2} m {v}^{2}$

This work done appears as kinetic energy (K) of the body.

hence

$k = \frac{1}{2} m {v}^{2}$

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