Question

proof that.
$s =ut + \frac{1}{2} a {t}^{2}$
​

Answer 1

$\longrightarrow\sf{\dfrac {dv}{dt}=a}$

$\longrightarrow\sf{dv=a\ dt}$

$\displaystyle\longrightarrow\sf{\int\limits_u^vdv=\int\limits_0^ta\ dt}$

$\longrightarrow\sf{\left [v\right]_u^v=a\left [t\right]_0^t}$

$\longrightarrow\sf{v-u=at}$

$\longrightarrow\sf{v=u+at}$

$\longrightarrow\sf{\dfrac{ds}{dt}=u+at}$

$\longrightarrow\sf{ds=(u+at)\ dt}$

$\displaystyle\longrightarrow\sf{\int\limits_0^sds=\int\limits_0^t(u+at)\ dt}$

$\longrightarrow\sf{\left [s\right]_0^s=u\left [t\right]_0^t+a\left [\dfrac {t^2}{2}\right]_0^t}$

$\longrightarrow\sf{\underline {\underline {s=ut+\dfrac {1}{2}at^2}}}$

Answer 2

$\huge{\bold{Heya\: Dost }}$

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$2nd Equation of Motion$

~ S=ut+1/2 at² It 2nd is equation of motion.

Here,

S = Displacement

u = initial velocity

t = time

a = acceleration