Question

Derive 3rd equation motion

Answer 1

Third equation of Motion

v^2 = u^2 +2as

sol.

We know that

V = u + at

=> v-u = at

or t = (v-u)/a ………..eq.(3)

Also we know that

Distance = average velocity X Time

.: s = [(v+u)/2] X [(v-u)/a]

=> s = (v^2 – u^2)/2a

=>2as = v^2 – u^2

or v^2 = u^2 + 2as

Answer 2

$\large\tt\underline\red{By\:kinametical\:3rd\:equation,}$

$\large\sf\red{v=u+at}$

$\large\sf\pink{ {v}^{2} = {(u + at)}^{2}}$

$\large\sf\pink{ {u}^{2} + 2u \: at + {a}^{2} {t}^{2}}$

$\large\sf\pink{{v}^{2}= {u}^{2} + 2a(ut + \frac{1}{2} {at)}^{2}}$

$\large\sf\pink{ {v}^{2} = {u}^{2} + 2as}$

$\large\star\tt\underline\purple{This\:is\:kinametical\:3rd\:equation}$