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 = 1/2mv2

Derivation : we know that

W = f x s

but f = ma

W = mas......-> Eqn 1

By 3rd Eqn of motion

v2 = u2 + 2as

at rest u=0

v2 = 2as

as = 1/2 v2

Putting in Eqn 1

W = 1/2 mv2

Since work done is stored in kinetic energy.

so, K E = 1/2 mv2

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 ....Eqn 1

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

F = mg and

s = h

then Eqn 1 becomes

W = mgh

Since work done = P.E

so P.E= mgh

Hope you get it :)

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