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Derive the expression for kinetic energy
Asked by jainnishka8 | 01 Dec, 2020, 06:17: PM
Kinetic energy of an object is energy associated with its motion.

From work-energy theorem , we know that workdone on the object equals change in kinetic energy.

Let F is the force acting on object to move the object by a distance d .

If m is mass of the object , which is initially at rest and a is the acceleration due to applied force ,

Then workdone W on the object = force × distance = mass  × acceleration × distance

W = m × a × d  ..................... (1)

if v is the final speed of object , then from equation of motion we get distance d as  ,

d = (v2 - u2 ) / (2a )  ....................(2)

where u is initial speed which is zero because we have assumed that object is initially at rest and a is acceleration

hence, acceleration d =  v2 / ( 2 a )  ................ (3)

By substituting d from eqn.(3) , we rewrite eqn.(1) as

W = m × a × [ v2 / (2a) ] = (1/2) m v2

In above equation RHS is kinetic energy of object.
Answered by Thiyagarajan K | 02 Dec, 2020, 10:18: AM

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