Question

Derive expression for kineic energy​

Answer 1

$\large\sf\underline{\underline{\color{cyan}{Solution :−}}}$

Consider a body of mass ‘m’ at rest.

Let a constant force F act on the body producing an

acceleration ‘a’ for a distance ‘s’.

Let the velocity of the body be changed to v.

In this case,

initial velocity = 0.

Final velocity = v

Using,

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

$\implies \: {v}^{2} = 0 + 2as \\ \implies {v}^{2} = 2as \\ \implies s = \frac{ {v}^{2} }{2a}$

Work done F×s

= mas = $ma \frac{ {v}^{2} }{2a}$

=> work done = 1/2 mv²

By definition this work done is equal to the kinetic energy.

$\therefore \: { \sf{ \color{blue}{kinetic \: energy \: of \: the \: body \: \: }}}{ \sf{ \color{red}{ = \frac{1}{2} {mv}^{2} }}}$

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Answer 2

v ² - u² = 2as… This statement states that a work W is done by a body to move from one position to another by a distance s when the force F is applied to a body at rest. This work done on the body is because of Kinetic energy (K.E) of the body.

T H A N K S :)