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    can you explain me kinetic eneergy formula derivation
Asked by seeni2005 | 14 Feb, 2016, 07:29: PM
answered-by-expert Expert Answer
The energy possessed by an object on account of its motion is known as kinetic energy.
Consider an object of mass m, moving with initial velocity u. Let it be displaced through a distance s when a constant force F acts on it in the direction of its displacement. The work done is
 W = F × s
The work done on the object will cause a change in its velocity. Let its velocity change from u to v. Let a be the acceleration produced.
We know that
begin mathsize 14px style straight v squared minus straight u squared equals 2 as therefore straight s equals fraction numerator straight v squared minus straight u squared over denominator 2 straight a end fraction end style
We also know that F = ma
 Thus, work done is
 begin mathsize 14px style straight W equals ma cross times fraction numerator straight v squared minus straight u squared over denominator 2 straight a end fraction space space space equals space 1 half straight m left parenthesis straight v squared minus straight u squared right parenthesis end style
 
Thus, we can say that work done is equal to the change in kinetic energy of the object.
If the object starts from rest, then u = 0. Thus, we have,
begin mathsize 14px style straight W equals 1 half mv squared equals straight E subscript straight k end style
Thus, the kinetic energy of a body is
  • Directly proportional to the mass of the body
  • Directly proportional to the square of the velocity of the body
Answered by Faiza Lambe | 15 Feb, 2016, 03:12: PM

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