Question

Derive third equation of motion.

Answer 1

We have to prove the third equation of motion

According to the third Equation of Motion

$v^2-u^2=2as$

Proof -

Let initial speed = u

Final speed = v

Acceleration = a

Time = t

From the first equation of motion

$v=u+at$

$Or,t=\frac{v-u}{a}$

Average velocity is given as

$\frac{v+u}{2}$

Also we know that

Distance = average velocity X Time

$s=\frac{v+u}{2}\times \frac{v-u}{a}$

After solving

We get

$v^2-u^2=2as$
This is the third equation of motion.

Hence proved.