Question

derive formula of kinetic energy in easy method

Answer 1

Suppose a Force ‘F’ acting on a body of mass ‘m’ in state of rest changes its velocity to ‘v’ and body covers ‘s’ distance in the direction of force.

Then, the work done by the force is given by

W = F . S

= ma . S …………(1) [ F = ma ]

Now, using equation of motion, we have

v2 = u2 + 2aS

or, v2 = 0 + 2aS

as = v2/2

So, by equation (1) , we get

W = m .v2/2

so , by definition of kinetic energy of the body,

K.E. = W = 1/2 mv2.

Answer 2

$\huge{hello-dear}$
→→→→→→→→→→→→→→→→→→→→→

Answer:  From equations of motion, the relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is   But from Newton’s second law of motion F = m a.work done by the force, F is written as the following: 
............... v^2-u^2
w = ma-------------- => w = 1/2m (v^2-u^2)
...... ... .. ....... 2a

If the object is starting from its stationary position, that is, u = 0, then 

w= 1/2m (v^2-0^2)=> w = 1/2m v^2 From work and energy theorem, work done is equal to the change in the kinetic energy of the object. w = (1/2) mv 2 If u = 0, the work done will be, Thus the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is  K.E = (1/2) mv 2..

#######################
Hope its help you ^_-