Question

(2)
3. (a) Derive the 2nd equation of motion using the graphical method​

Answer 1

Given :

• Derive the second equation of motion using the graphical method

According to the question,

The second equation of motion is :

$\star \boxed{ \sf \purple{s = ut + \frac{1}{2} {at}^{2} }}$

• s stands for Distance
• u stand for Initial velocity
• t stands for Time
• a stands for Acceleration

$\sf \leadsto{s = Area \: of \: trapezim \: OABCD}$

$\leadsto \sf{s = Area \: of \: rectangle + Area \: of \: triangle }$

$\sf \leadsto{s = OD \times CD + \frac{1}{2} \times AC \times CB }$

$\leadsto \sf{s = t \times u + \frac{1}{2} \times t \times (v - u) } \: \: \: \: \: \: \: \: ...(v - u = at)$

$\leadsto \sf{s =ut + \frac{1}{2} \times t \times at }$

$\leadsto \boxed{\sf{s = ut + \frac{1}{2} {at}^{2} }} \green \bigstar$

Note : For diagram refer to the attachment..