Question

Define kinetic energy ? Derive a relation between kinetic energy and mass and velocity of an object ?

Answer 1

The energy possessed by a body because of its motion is called Kinetic energy of the that body.
K=(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 of all 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.

Answer 2

energy which a body possesses by virtue of being in motion.
Relation between them
K. E=1/2*m*v square