# derive an expression for kinetic energy of a body ?

Hi,

Energy by virtue of its motion is called as kinetic energy. An object that has motion, whether it may be vertical or horizontal motion, has kinetic energy. Kinetic energy depends on mass (m) of the object and speed (v) of the object. The equation used to represent kinetic energy is:

KE = ½ mv2

Derivation of the formula :-

Let a body of massmbe moving with a uniform velocityu. Let an external force be applied on it so that it displaces a distancesand its velocity becomesv.

We have velocity-position relation as

v 2=u 2+ 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 tov, we obtain

Kinetic energy,

• -5

Derivation of kinetic energy:-

workdone by the force is F.S

F=m.a

WD=m.a.s --------1equation

From the equation of motion, we have,

v2 - u2 =2as

As the body was initially at rest so u=0

v2 =2as

1/2 v2= as------------2 equation

Putting the value of as from 2 equation to 1 equation we get,

WD= 1/2 mv2

This work done by the force is equal to the kinetic energy of the body which is called as the kinetic energy.

KE= 1/2 mv2

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