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Question
The velocity of a body moving in a straight line is increased by applying a constant force F, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.
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Solution
Let the body covers a distance s when a constant force F is applied in the direction of motion.
Work done by this force, W = F. s
Let the velocity of the object of mass m change
from u to v with acceleration and on application
of constant force F, then F = ma
From equation of motion, v2 − u2 = 2as, we get
s = `("v"^2 - "u"^2)/(2"a")`
∴ W = Fs = ma `(("v"^2 - "u"^2)/(2"a"))`
= `1/2 "mv"^2 - 1/2 "mu"^2`
= final kinetic energy – initial kinetic energy
= change in kinetic energy
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