what is the derivation of kinetic energy ?

Kinetic energy - The energy possessed by virtue of its motion is said to be kinetic energy.

K E = 1/2mv²

Derivation : We know that,

W = f x s          

but f = ma

W = mas    ….. (1)

By 3^rd eqⁿ of motion,

v² = u² + 2as

at rest, u=0

v² = 2as

as = 1/2 v²

Substituting in eqⁿ 1, we get,

W = 1/2 mv²

Since work done is stored in kinetic energy.

so, K.E. = 1/2 mv²