Question

derivation of kinetic energy​

Answer 1

Explanation:

we know that

work done = Force × displacement

w= Fs -------(1)

from 3rd eq of motion

v²-u²= 2as

s=v²-u²/2a--(2)

Also F= ma---(3)

putting value of eq 3 and 2 in eq 1 we get

W= ma×v²-u²/2a

the a will cancel each other and let the body starts from rest so u = 0

W= mv²/2 or 1/2mv²

also W= Ek ( Ek is kinetic energy as work done is directly proportional to energy)

so

Ek= 1/2mv²

Answer 2

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

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

$\mathsf{\implies Work done = Fs}$

$\mathsf{\implies v² = u² + 2as}$

$\mathsf{\implies s = \frac{v² - u²}{2a}}$

$\mathsf{\implies u = 0 m/s \: for \:a \: body \: starting \: from \: rest}$

$\mathsf{\implies Work \: Done = \: Energy}$

$\mathsf{\implies Kinetic \: Energy \: is \: also \: written \: as \: E_k}$

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

$\mathsf{Derivation}$

$\mathsf{\hookrightarrow E_k = Work done = Fs }$

$\mathsf{\hookrightarrow \: = \: Fs \: = ma × s }$

$\mathsf{\hookrightarrow E_k = m × \frac{v² - u²}{2a} × s}$

$\mathsf{\hookrightarrow E_k = \frac{1}{2}mv²}$