Question

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

Answer 1

Answer:

when initial speed is 0.

Step-by-step explanation:

initial speed = 0 , (u)

distance = s

time = t

final speed =v

According to the question:

s = (u+v)2

s = ut + 1/2 at²

(u+v) = at

therefore:-

=(u+v/2)t = ut + 1/2at²

=(at/2)t = 0t + 1/2at²

=1/2at² = 1/2at²

Answer 2

Need To Do :-

• How can we say that s = ut + 1/2at² .

$\red{\frak{Given}}\Bigg\{ \sf s = ut +\dfrac{1}{2}at^2$

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 ,

$\sf\longrightarrow v = u + at$

where ,

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

Now , we know that ,

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