Question

Derive second equation of motion:
$s=ut+\frac{1}{2}a{t}^2$

Answer 1

We have to prove the second equation of motion

Let the distance traveled by the body be “s”.
We know that
Distance = Average velocity $\times$ Time
Also, Average velocity = $=\frac{u+v}{2}$

So we can write
$\therefore Distance\left(t\right)=\frac{u+v}{2}\times t$ . . . . . eq. (1)
From the first equation of motion

We know that:

v = u + at
substituting this value of “v” in eq.(1), we get
$s=\frac{(u+u+at)}{2}\times t$

Or,
$\Rightarrow s=\frac{(2u+at)}{2}\times t$

Or,
$\Rightarrow s=\frac{(2ut+a{t}^2)}{2}$

Or,
$\Rightarrow s=\frac{2ut}{2}+\frac{a{t}^2}{2}$
$ors=ut+\frac{1}{2}a{t}^2$

This is the 2nd equation of motion.

Hence proved.