Question

derive kinetic energy = 1/2 m v^ v square

Answer 1

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". ThenFirst of all we will find the acceleration of body.Using equation of motion2aS = Vf2 – Vi2 
Putting the above mentioned values 
2ad = V2 – 0
a = V2/2dNow force is given by
F = ma 
Putting the value of acceleration
F = m(V2/2d) 
As we know that 
Work done = FdPutting the value of F
Work done = (mv2/2d)(d)
Work done = mV2/2
OR 
Work done = ½ mV2Since the work done is motion is called "Kinetic Energy"
i.e. 
K.E. = Work done 
OR 
K.E. =1/2mV2.  
Hope This Helps.