Derive the formula: K=1/2mv^2 where K …
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Gaurav Seth 6 years, 5 months ago
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.
3Thank You