Question

Find the correctness of S =Ut +1/2atsquare.

Answer 1

To Prove:  $\bold{{ S }={ ut }+\frac { 1 }{ 2 } { at }^{ 2 }}$

We know that,  $\bold{Average\:\: Velocity=\frac { total\:\:distance\:\:travelled }{ total\:\: time\;\:taken }}$

$\bold{Average\:\:Velocity =\frac { S }{ t }}$

Average velocity is also written as $\bold{{ u }+{ \frac { v }{ 2 } }}$

By equating both the above equations

$\frac { S }{ t } =u+\frac { v }{ 2 }$

We know that , "first equation of motion" v = u+at

By substituting the value of 'v' in equation 1, we get

$\bold{\frac { S }{ t } ={ u }+\frac { { u }+{ at } }{ 2 }}$

By simplifying, $\bold{S=\left( \frac { 2u+at }{ 2 } \right) t}$

$\bold{S=\frac { 2ut+a{ t }^{ 2 } }{ 2 }}$

$\boxed{\bold{\therefore{ S }={ ut }+\frac { 1 }{ 2 } { at }^{ 2 }}}$