Question

PLEASE PROOF ALL EQUATIONS OF MOTION.
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PLEASE ANSWER CORRECTLY AND BEWARE OF SPAMMING!

Answer 1

$\rm\color{palevioletred}{\underline{1.\: First \:equation \:of \:motion \: :- }}$

v = u + at

$\sf{ \: we \: know \: acceleration(a) \: = \frac{change \: in \: velocity}{time \: taken} }$

$\sf{ a \: = \frac{final \:velocity \: - \: initial \:velocity}{time \: taken} }$

$\sf{or \: \: \: \: a = \frac{v - u}{t} } \\ \sf{or \: \: at = v - u} \\ \fbox{\sf{ \therefore \: v = u + at}} \: ....(1)$

$\rm\color{palevioletred}{\underline{2.\: Second \:equation \:of \:motion \: :- }}$

$\sf{s =ut + \frac{ 1}{2}{at}^{2} }$

We know ,

$\sf{\implies Distance \:travelled = Average\: Velocity × Time}$

$</p><p>\sf{ Distance \: travelled =\frac{Initial \: Velocity+Final \: Velocity}{2}×Time}</p><p>$

$\sf{s=\frac{v+u}{2}×t}$

From equation (1) $\implies$v = u+at

$\sf{\therefore s =\frac{ u+(u+at)}{2}×t}$

$\sf{or \: \: s =\frac{ 2u+at}{2}×t}$

$\fbox{ \sf{s =ut + \frac{ 1}{2}{at}^{2} }} \: .....(2)$

$\rm\color{palevioletred}{\underline{3.\: Third \:equation \:of \:motion \: :- }}$

$\sf{Distance\: travelled = Average\: Velocity ×\: Time}$

$\sf{Distance \:travelled\: =\frac{Initial\:Velocity\:+\:Final\:Velocity}{2}×Time}$

$\sf{ \implies s= \frac{v+u}{2}×t}$

From equation (1) $\implies$v=u+at

$\sf{or \: t= \frac{v-u}{a}}$

$s= \frac{v+u}{2} × \frac{v-u}{a}$

$\implies\sf{s = \frac{ {v}^{2} - {u}^{2} }{2a} }$

or v²-u² = 2as

$\sf\fbox{{v}^{2}= {u}^{2}+2as }$.....(3)

Answer 2

Explanation:

Refer to the attachment