Question

Prove that kinetic energy is the half of the product of mass and square of velocity

Answer 1

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.