Question

prove
${v}^{2} - {u }^{2} = 2as$
​

Answer 1

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

Answer 2

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 .....