Question

.prove : s=ut +½ at²​

Answer 1

Explanation:

Let the distance covered by the body be s, initial and final velocities be u and v respectively and time taken be t.

$\therefore Average\: velocity = \frac{u+v}{2} \\\\Now, \:we \:know\: that\\\\Distance \:covered\\ = Average\: velocity \times time\\\\\therefore s= \frac{(u+v) }{2} \times t..... (1)$

By first equation of motion:

$v = u + at$

Substituting the value of v in equation (1), we find:

$s= \frac{(u+u + at)}{2} \times t\\\\\therefore s= \frac{(2u + at)}{2} \times t\\\\\therefore s= \frac{(2ut + at^2)}{2}\\\\\therefore s= \frac{2ut} {2}+ \frac{at^2}{2}\\\\ \huge \orange {\boxed {\therefore s= ut+ \frac{1}{2}at^2}}$

Hence proved.