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Expression for kinetic energy :
Suppose a Force ‘F’ acting on a body of mass ‘m’ in state of rest changes its velocity to ‘v’ and body covers ‘s’ distance in the direction of force.
Then, the work done by the force is given by
W = F . S
= ma . S …………(1) [ F = ma ]
Now, using equation of motion, we have
v2 = u2 + 2aS
or, v2 = 0 + 2aS
as = v2/2
So, by equation (1) , we get
W = m .v2/2
so , by definition of kinetic energy of the body,
K.E. = W = 1/2 mv2
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