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 = 1/2 mv^{2}

Derivation: We know that,

W = f x s

but f = ma

W = mas …… (1)

By 3^{rd} eq^{n} of motion,

v^{2} = u^{2} + 2as

at rest, u=0

v^{2} = 2as

as = 1/2 v^{2}

Substituting in eqn 1, we get,

W = 1/2 mv^{2}

Since work done is stored in kinetic energy.

so, K.E. = 1/2 mv^{2}