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kompoz [17]
4 years ago
10

.prove : s=ut +½ at²​

Physics
1 answer:
o-na [289]4 years ago
6 0

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.

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