Question

Derive equation of motion, S = ut + 1/2 at2 (position – time relation)    graphically for uniformly accelerated motion.​

Answer 1

Question-

Derive the equation of motion, S = ut + 1/2 at2 (position-time relation)    graphically for uniformly accelerated motion.​

Answer-

For the given graph, we can say that

$displacement=\dfrac{1}{2}\times (OA+BC)\times (OC)$

Substituting the values of the mentioned sides, we get

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

Substituting the value of the final velocity from the first equation and simplifying, we get

$\begin{align}& s=\dfrac{1}{2}\times (u+u+at)\times (t) \\& \Rightarrow s=\dfrac{1}{2}\times \left( 2ut+a{{t}^{2}} \right) \\& \Rightarrow s=ut+\dfrac{1}{2}a{{t}^{2}} \\\end{align}$

This is the second equation of motion.

Hence, derived