Question

derivation of kinetic energy class 9

Answer 1

let the body of mass M kg is moving with velocity V M / s
work done to stop body equals kinetic energy of the body
from third equation of motion
v²=u²+2as
a=v²-u²/2s
here u = 0
a=v²/2s.. ............(i)
work done = FS
= m x a x s......... .....( F =m x a)
from equation 1
kinetic energy =mxv²/2sxs
= mv²/2
hence kinetic energy = mv²/2

Answer 2

Kinetic Energy derivation:

• Let's assume that initial velocity of object is zero (v) and final velocity is u :

Now, applying Work Energy Theorem :

$\boxed{W=\Delta KE = F s = (ma)s}$

Now, from equations of kinematics, we know :

$\boxed{{v}^{2} = {u}^{2} + 2as}$

$\implies \: as = \dfrac{ {v}^{2} - {u}^{2} }{2}$

Now, putting this value :

$\implies \Delta KE = \dfrac{m( {v}^{2} - {u}^{2} )}{2}$

Now, initial velocity (u) and KE is zero.

$\implies KE = \dfrac{m( {v}^{2} - {0}^{2} )}{2}$

$\boxed{ \implies KE = \dfrac{m {v}^{2} }{2}}$

[Hence derived]