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  • 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.

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.

By the equation of motion, we can say:
v^{2}=u^{2}+2as
\Rightarrow s=\frac{v^{2}-u^{2}}{2a}

By Newton’s second law, we can say:
F= ma 
We know that work done is defined as the product of force and displacement if the body is moving on a straight track.
W=Fs
\Rightarrow W=ma\times \frac{v^{2}-u^{2}}{2a}
\Rightarrow W=m\times \frac{v^{2}-u^{2}}{2}
\Rightarrow W=\frac{mv^{2}}{2}-\frac{mu^{2}}{2}
\Rightarrow W=KE_{f}-KE_{i}
Hence, work done is equal to the change in kinetic energy.

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