**Definition**

“Energy posses by a body by virtue of its motion is referred to as ‘Kinetic Energy’”.

**Formula**

K.E. = 1/2 mv2

Kinetic energy depends upon the mass and velocity of body.

If velocity is zero than K.E. of body will also be zero.

Kinetic energy is a scalar quantity like other forms of energies.

**Derive:** K.E = 1/2 mv2

**Proof**

Consider a body of mass “m” starts moving from rest. After a time interval “t” its velocity becomes V.

If initial velocity of the body is Vi = 0 ,final velocity Vf = V and the displacement of body is “d”. Then

First we will find the acceleration of body.

Using equation of motion

2aS = Vf2 – Vi2

Putting the above mentioned values

2ad = V2 – 0

a = V2/2d

Now force is given by

F = ma

Putting the value of acceleration

F = m(V2/2d)

As we know that

Work done = Fd

Putting the value of F

Work done = (mv2/2d)(d)

Work done = mV2/2

OR

Work done = ½ mV2

Since the work done is motion is called “Kinetic Energy”

i.e.

K.E. = Work done

OR

K.E. =1/2mV2.

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