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Prove: st = ut+½ at²​

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Step-by-step 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 = (u+v)/(2) \\\\ Now, \:we \:know\: that\\\\ Distance \:covered\\ = Average\: velocity * time\\\\ \therefore s= ((u+v) )/(2) * t..... (1)\\\\

By first equation of motion:


v = u + at

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


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

Hence proved.

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