Question

how s=(u+v/2)t. equal to. s=ut+1/2 at2​

Answer 1

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given :- }}}}$

• A equation , s = ( u + v /2 ) t

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To Do :- }}}}$

• How can we say that s = ( u + v / 2 ) t = ut + 1/2 at² .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution :- }}}}$

The given equation is the Second equation of motion . It is also known as Position time relation . Here we will make use of First equation of motion as ,

$\sf\dashrightarrow v = u + at$

where ,

• a is the acceleration .
• u is the initial Velocity .
• v is final velocity .
• t is the time elapsed .

Now , we know that ,

$\sf\dashrightarrow Displacement = Average \ velocity * Time \ elapsed \\\\\\\sf\dashrightarrow s = \bigg(\dfrac{u+v}{2}\bigg) * t \\\\\\\sf\dashrightarrow s = \bigg( \dfrac{ u + u + at }{2}\bigg)*t \qquad \bigg\{ \red{ From \ First \ equ^n \ of \ motion }\bigg\} \\\\\\\sf\dashrightarrow s = \bigg(\dfrac{ 2u + at }{2}\bigg)*t \\\\\\\sf\dashrightarrow s = \dfrac{2u}{2}*t + \dfrac{at*t}{2} \\\\\\\sf\dashrightarrow \underset{\blue{\sf Hence \ Proved }}{\underbrace{\boxed{\pink{\frak{ s= ut + \dfrac{1}{2}at^2}}}}}$