Physics, asked by vinu0000, 1 year ago

derive the equation v²= u²+2as

Answers

Answered by kaushik12

Hello freind !!
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When a body is moving with uniform acceleration , the distance travelled by the body is given by :

Distance = Average velocity × time .........(1)

If u and v are the initial and final velocity then one can write

s = { v + u /2}×t ........(2)

By the first equation of motion ,

v = u + at

this gives

t = { V- U /a}

substituting the value of t in the equation ....2)we get

s = ( v + u /2) × (V- U/a)

this gives

2as = v^2 - u^2

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Answered by aayyuuss123

Explanation:

$\huge\boxed {\pink {\mathbb{\underline {Answer}}}}$

From the 1st equation of motion...

$V=U+at\\</p><p>V-U=at\\</p><p>\frac{V-U}{a}=t\\</p><p>t=\frac {(V-U}{a)}$

Put the value in the 2nd equation of motion..

$S=\frac {1}{2}(V+U)\frac{V-U}{a}\\</p><p>S=\frac {1}{2a}(V^2-U^2)\\</p><p>2aS=V^2-U^2\\</p><p>\implies V^2-U^2=2aS\\</p><p>\implies V^2=U^2+2aS</p><p>$

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