derive an expression for kinetic energy of a body - Science - Work and Energy

Question

derive an expression for kinetic energy of a body ?

Vyshnav Veenus · Accepted Answer

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,

(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,