Question

Relation between work done and kinetic energy derivation

Answer 1

I Hope it will help you.....

Answer 2

$\bold{Work\: Energy\: Theorem}$

This theorem states that the $\small\bold{work\: done\: by\: a\: net\: force\: in\: displacing\: a\: body\: is\: equal\: to\: change\: in\: kinetic\: energy\: of\: the\: body}$

We consider a body of mass mm moving with initial velocity $u$ .

Let a force F be applied on the body, so that it acquires some acceleration $a$ such that..

F = $ma$

If the body is displaced through a distance $d$ along the direction of the force , then

W = F$d$ Cos0° = $mad$ .....(1)

If the body acquires velocity $v$ after travelling a distance $d$ , then from equation of motion, we have

v² - u² = 2ad

or a = (v² - u²)/2d

on substituting value of a in equation (1). we get,

W = m[(v² - u²)/2d]d

or

W = (1/2)mv² - (1/2)mu²

It's just similar to the formula of △K.E

so by following this,

△K.E. = W

Hence proved...

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