Question

derive equation kinetic energy​

Answer 1

Answer:

Let the velocity of an object of mass 'm' changes from 'u' to 'v' where a constant force 'f' is acts on it .

Also let 'a' be the acceleration produced and 's' be the distance covered.

we know ,

v2=u2+2as

=v2-u2=2as

s=v2-u2/2as .....eq1

work done by the force F on the object is given by:

w=f×s

=ma×s

=ma(v2-u2/2a). [using 1].

=1/2 m(v2-u2)

If the object starts from rest ,then u=0

therefore w=1/2mv2.

This works done is converted to the kinetic energy of the object .

therefore EK=1/2mv2.

Answer 2

The energy produced by a body due to the virtue of its motion is called kinetic energy.

${ \green{ \bf{ Derivation \: of\: kinetic \:energy:- }}}$

Let,

m=mass of a body at rest

F=force applied on the body

s=displacement in the direction of force

v=final velocity of the body

As, v²=u²+2as

v²=0²+2as

v²=2as

s=v²/2a

Then,

Work=fs

W=F×S

W=ma×v²/2a

W= mv²/

K = 1/2mv²