Question

 s=ut+1/2at^2 prove it​

Answer 1

Let,

u=initial velocity

t=Time Taken

a=Acceleration

v=Final velocity

Now,

Inserting the formula of avg. speed, we get,

$\: \: \: \: \: \: \: average \: speed = \frac{u + v}{2} \times t$

$\: \: \: \: \: \: \: s = \frac{ut + vt}{2}$

Inserting v=u+at we get,

$\: \: \: \: \: \: \: s = ( \frac{u + u + at}{2} ) \times t$

$\: \: \: \: \: \: \: s = ( \frac{2u + at}{2} ) \times t$

$\: \: \: \: \: \: \: s = ( \frac{2u}{2} + \frac{at}{2} ) \times t$

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

☆☆☆Hence,It is proved..☆☆☆