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Derive kinetic energy by calculus method …

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Derive kinetic energy by calculus method

 

  • 1 answers

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 F = ma 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" />

 

K = W

Rewrite work as an integral: we can represent the work done in terms of a velocity differential.

K = F. dr

Rewrite force in terms of velocity: mass is a scalar and can therefore be factored out.

 

K = ma.dr

=> K = ma.dr

=> K = mdvdt.dr

=> K = mdrdt.dv

=> K = mv.dv

=> K = 12mv2

 

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