Two particles of equal mass have velocities $\overrightarrow{{\mathrm{v}}_1}=4\hat{\mathrm{i}}{\mathrm{ms}}^{-1}$ and $\overrightarrow{{\mathrm{v}}_2}=4\hat{\mathrm{j}}{\mathrm{ms}}^{-1}$. First particle has an acceleration $\overrightarrow{{\mathrm{a}}_1}=\left(5\hat{\mathrm{i}}+5\overrightarrow{\mathrm{j}}\right) {\mathrm{ms}}^{-2}$, while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

Since, ${\mathrm{m}}_1={\mathrm{m}}_2=\mathrm{m}{\overrightarrow{\mathrm{v}}}_{\mathrm{cm}}=\frac{{\mathrm{m}}_1{\overrightarrow{\mathrm{v}}}_1+{\mathrm{m}}_2{\overrightarrow{\mathrm{v}}}_2}{{\mathrm{m}}_1+{\mathrm{m}}_2}=\frac{\mathrm{m}}{2\mathrm{m}}\left({\overrightarrow{\mathrm{v}}}_1+{\overrightarrow{\mathrm{v}}}_2\right)=\frac{1}{2}\times \left(4\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)$

$\mathrm{acceleration} \mathrm{of} \mathrm{center} \mathrm{of} \mathrm{mass}$

$=\frac{5}{2}\times \left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)$

Both ${\overrightarrow{\mathrm{v}}}_{\mathrm{cm}}={\overrightarrow{\mathrm{a}}}_{\mathrm{cm}}$ are parallel centre of mass will move in a straight line because velocity and acceleration of centre of mass are in the same direction.