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Question
A body of mass m is moving with a uniform velocity u. A force is applied on the body due to which its velocity changes from u to v. How much work is being done by the force?
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Solution
The body of mass m is moving with a uniform velocity u.
A force is applied on the body due to which its velocity changes from u to v and produces an acceleration a in moving a distance S.
Then, Work done by the force = force × displacement
W = F × S ...(i)
From relation : v2 = u2 + 2 a S
Displacement, S =`(v^2-u^2)/(2a)`
And force, F = ma
From equation (i), W = `ma xx ((v^2-u^2)/(2a))`
=`1/2m(v^2-u^2)`
= K1 - K2
Where K1 is the initial kinetic energy = `1/2 mv^2`
And K2 is the final kinetic energy = `1/2 mv^2`
Thus, work done on the body = Increase in kinetic energy
W = `1/2 m(v^2 - u^2)`
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