Question

formula of kinetic energy and proof

Answer 1

K. E=1/2mvsquare is your answer

Answer 2

Formulae of kinetic energy = 1/2 mv²

$\bold{Derivation}$
Let an object of mass = m
is moving with final velocity = v
It's initial velocity = u
acceleration of the object = a

We know that ,
W = F * s .......(1.)

Where W=work,F = force,s=displacement

Now ,
F = m * a .......(2.)

From Newton's 3rd equation of motion .

v² - u² = 2as

s = v² - u²/ 2a ......(3.)

Now , put eq(2.) nd (3.) in eq.(1.)

W = m*$\cancel{a}$ * v² - u²/ 2$\cancel{a}$

W = m * v² - u² / 2

=> 1/2m(v² - u² )

If the object is starting from rest then it's initial velocity will be = 0

=>1/2m(v² - 0)

K.E. = 1/2 mv²

"proved"