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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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the formula of ke is 1/2 mv2 and potential energy is mgh.hope it helps thumbs up plzzz...

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Formula for kinetic energy

Kinetic energy of a moving body is equal to the work required to change its velocity from u to v.

Let a body of mass m be moving with a uniform velocity u. Let an external force be applied on it so that it displaces a distance s and its velocity becomes v.

We have velocity-position relation as

v2 = u2 + 2as

where, a → acceleration of the body during the change of velocity

Or  … (1)

Hence, work done on the body by the force will be given by,

W = F × s

F = ma

W = 

If the body was initially at rest, i.e. u = 0, then

W

Since kinetic energy is equal to the work done on the body to change its velocity from 0 to v, we obtain

Kinetic energy, 

Hence, kinetic energy of a body increases with its velocity. Its SI unit is Joule (J).

P.E.:

since, W=FxS

bt F=ma

and on height s=h 

therefore, W=Mxgxh

bt, it is a at rest so it possess potential energy

therefore P.E.=Mgh

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