The first equation of motion is \(v=u+a t\).
\(v-u=\) at \(\ldots\) (1)
Average velocity \(=\frac{5}{t} \quad \ldots(2)\)
Average velocity \(=\frac{u+v}{2} \quad \cdots\) (3)
From equation (2) and equation (3) we get, \(\frac{u+v}{2}=\frac{S}{t}\)
Multiplying equation (1) and equation (4) we get, \((v-u)(v+u)=a t \times \frac{2 S}{t}\)
\((\mathrm{v}-\mathrm{u})(\mathrm{v}+\mathrm{u})=2 \mathrm{aS}\)
[We make use of the identity \(\left.a^{2}-b^{2}=(a+b)(a-b)\right]\) \(\mathrm{v}^{2}-\mathrm{u}^{2}=2 \mathrm{aS} \quad\) III equation of motion
