Derive kinetic energy by calculus method …
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Naveen Sharma 8 years, 4 months ago
Ans. When there are no opposing forces, a moving body tends to keep moving with a steady velocity as we know from Newton's first law of motion. If, however, a resultant force does act on a moving body in the direction of its motion, then it will accelerate per Newton's second law The work done by the force will become converted into increased kinetic energy in the body.
Derivation Using Calculus :
Begin with the Work-Energy Theorem : The work that is done on an object is related to the change in its kinetic energy<meta aria-hidden="true" />
Rewrite work as an integral: we can represent the work done in terms of a velocity differential.
Rewrite force in terms of velocity: mass is a scalar and can therefore be factored out.
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1Thank You