Question

Derive each and every Equation of motion for class 9th ​

Answer 1

$\textbf{Answer is in Attachment !}$

Answer 2

$\huge\underline{\bold{\red{Answer\::}}}$

$\underline{\bold{1st\:equation\:of\:motion\::}}$

a = uniform acceleration

s = distance travelled

u = initial velocity

v = final velocity

t = time

$Acceleration$ = $\dfrac{Change\:in\:velocity}{Time\:taken}$

= $\dfrac{BD}{OA}$ = $\dfrac{AD\:-\:AB}{OA}$

$a$ = $\dfrac{v\:-\:u}{t}$

at = v - u

$\boxed{\boxed{v\: =\: u\: + \:at}}$

$\underline{\bold{2nd\:equation\:of\:motion\::}}$

s = OA × AB + $\dfrac{1}{2}$ × CB × BD

s = t × u + $\dfrac{1}{2}$ × t × at

$\boxed{\boxed{s\:=\:ut\:+\:{\dfrac{1}{2}\:a{t}^{2}}}}$

$\underline{\bold{3rd\:equation\:of\:motion\::}}$

s = $\dfrac{1}{2}$ (OC + AD) (OA)

s = $\dfrac{1}{2}$ (u + v) × $\dfrac{v\:-\:u}{a}$

s = $\dfrac{1}{2a}$ (v² - u²)

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

$\boxed{\boxed{2as\:=\:{v}{^2}\:-\:{u}^{2}}}$