Physics - Kinematics Question with Solution | TestHub

Portion OA, OB corresponds to motion with acceleration ' $\mathrm{f}$ ' and retardation ' $r$ ' respectively. Area of $△OAB=S$ and $OB=t$. Let $OL=t_1$, $\mathrm{LB}={\mathrm{t}}_2$ and $\mathrm{AL}=\mathrm{v},\mathrm{S}=\frac{1}{2}\mathrm{OB}\cdot \mathrm{AL}=\frac{1}{2}\mathrm{t}\cdot \mathrm{v};\mathrm{v}=\frac{2\mathrm{S}}{\mathrm{t}}$ Also, $\mathrm{f}=\frac{\mathrm{v}}{{\mathrm{t}}_1},{\mathrm{t}}_1=\frac{\mathrm{v}}{\mathrm{f}}=\frac{2\mathrm{s}}{\mathrm{tf}}$ and $\mathrm{r}=\frac{\mathrm{v}}{{\mathrm{t}}_2},{\mathrm{t}}_2=\frac{\mathrm{v}}{\mathrm{r}}=\frac{2\mathrm{s}}{\mathrm{tr}};\mathrm{t}={\mathrm{t}}_1+{\mathrm{t}}_2=\frac{2\mathrm{s}}{\mathrm{tf}}+\frac{2\mathrm{s}}{\mathrm{tr}}$ $t=\left(\frac{1}{f}+\frac{1}{r}\right)\frac{2s}{t}\Rightarrow t=\sqrt{2s\left(\frac{1}{f}+\frac{1}{r}\right)}$