Physics, asked by jack0259K, 10 months ago

prove
 {v}^{2}  -  {u }^{2}  = 2as

Answers

Answered by streetburner
3

Explanation:

v=u+at

at = v - u

And :

t = (v-u)/a

s = u(v-u)/a + 0.5at²

s = (uv-u²)/a + 0.5a*(v-u)²/a²

2as = 2uv-2u² + v² + u² -2vu

2as = v² - u²

Answered by rudra09
15

Answer:

Frm second law of motion can be obtain by eliminating t between the first two equations of motion .

This is done as follows .

From second law of motion we have :

s = ut +  \frac{1}{2}  \times at ^{2} ........(1)

And from first equation of motion

v = u + at.........(2)

This can be rearranged as ⤵

at = v - u \\

or

t =  \frac{v - u}{a}

Putting the value of t in equation( 1) we get

s =  \frac{v(v - u)}{a}  +  \frac{1}{2} a( \frac{v - u}{a} ) ^{2}

 s =    \frac{uv - u ^{2} }{a}  +  \frac{a(v ^{2} + u ^{2}  - 2uv) }{2a ^{2} }

s =  \frac{2uv - 2u ^{2}   + v ^{2} + u ^{2}  - 2uv }{2a}

2as \:  = v ^{2} - u ^{2}

v ^{2}  = u^{2}   + 2as

proved .....

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