Question

Prove that KE = 1/2mv^2

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.

Answer 2

First of all 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.
Hope it helps u!!