Explanation:
Let the distance covered by the body be s, initial and final velocities be u and v respectively and time taken be t.
[tex] \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)\\\\[/tex]
By first equation of motion:
[tex] v = u + at[/tex]
Substituting the value of v in equation (1), we find:
[tex] 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}} \\\\[/tex]
Hence proved.
