Question

Prove that the kinetic energy of a body moving with speed v is equal to 1/2mv^2

Answer 1

We have the third kinematic equation,

$v^2=u^2+2as\\\\a=\dfrac {v^2-u^2}{2s}$

But the force,

$F=ma\\\\\\F=m\left (\dfrac {v^2-u^2}{2s}\right)$

Well, the work done on a body by this force,

$W=Fs\\\\\\W=m\left (\dfrac {v^2-u^2}{2s}\right)s\\\\\\W=\dfrac {m(v^2-u^2)}{2}\\\\\\W=\dfrac {1}{2}mv^2-\dfrac {1}{2}mu^2$

Let $u=0.$ So,

$W=\dfrac {1}{2}mv^2$

This work done is stored in the body as its kinetic energy.

Hence Proved!