What is the derivation of Kinetic energy and Potential energy

Kinetic energy - The energy possessed by virtua of its motion is said to be kinetic energy. K E = 1/2mv^{2}

Derivation : we know that

W = f x s

but f = ma

W = mas......-> Eq^{n }1

By 3rd Eq^{n} of motion

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

at rest u=0

v^{2} = 2as

as = 1/2 v^{2}

Putting in Eq^{n} 1

W = 1/2 mv^{2}

Since work done is stored in kinetic energy.

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

Potential Energy - The energy possessed by virtua of its position is said to be potential energy. P E =mgh

Derivation: we know that

W = f x s ....Eq^{n} 1

when the object of mass m is lifted at a height h then,

F = mg and

s = h

then Eq^{n} 1 becomes

W = mgh

Since work done = P.E

so P.E= mgh

Hope you get it :)

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