Question

Formula for Kinetic Energy ?

Answer 1

1/2 mv^2 is the formula for kinetic energy

Answer 2

$\mathfrak{\underline{\underline{Formula\:for\:kinetic\:energy:-}}}$

If an object of mass 'm' moving with uniform velocity 'u' it is displaced through a distance's', constant force 'f' act on it in the direction of displacement. It's velocity changes from U to V.

$\implies$$\sf{The\:acceleration\:is\:'a'\:than}$

$\sf{Work\:done\:'W'\:F×S}$-------1.

$\sf{We\:know\:from\:2nd\:law,\:f=ma}$-----------2.

$\sf\underline{According\:to\:3rd\:equation\:of\:motion}$

$\sf{v^2-u^2=2as}$

s=$\sf\frac{v^2-u^2}{2as}$-------3.

Putting the values of F and S from equation (ii) & (iii) in equation (i)

W=m$\sf\cancel{a}$×$\sf\frac{v^2-u^2}{2\cancel a}$

W=$\sf{1}{2}m(v^2-u^2)$

If u=a (when body starts moving from rest)

$\sf{W=}$$\sf\frac{1}{2}m(v^2-a)$

$\sf{W=}$$\sf\frac{1}{2}mv^2$

$\bold{\large{\boxed{\sf{\pink{K.E=\frac{1}{2}mv^2}}}}}$