Question

derive third equation of motion with the help of first and second equation of motion . note that it has to be solved by using first and second equation of motion . [S²=U²+aS]​

Answer 1

Answer:

$second \: equation \: of \: motion = \\ s \: = ut + \frac{1}{2} a {t}^{2}$

$= s = (u + \frac{1}{2}a {t}) \times t$

$= s =( u + \frac{1}{2}( v - u)) \times t$

$= s = ( \frac{2u + v - u}{2} ) \times t$

$= s = ( \frac{v + u}{2} ) \times t$

$First \: equation \: of \: motion \: = \\ a \: = \frac{v - u}{t}$

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

Substituting t in the deduced second equation of motion

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

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

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

Hence, 2as = v²-u² is the third equation of motion

Hope it helps!!