Two particles of the same mass are moving towards each other with velocities $2v$ and $v$ respectively. The velocity of the centre of mass of the system is:

Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration $\vec{f}$. The centre of mass has an acceleration

Two particles of masses $3 \ kg$ and $6 \ kg$ are approaching towards each other with accelerations $2 \ m/s^2$ and $4 \ m/s^2$ respectively,on a smooth horizontal surface. Then the acceleration of the centre of mass of the system is ..... $m/s^2$.

$A$ system consists of two particles of masses $m_1$ and $m_2$ separated by a distance $r$. If the particles move towards each other with velocities $v_1$ and $v_2$ respectively,the velocity of the centre of mass of the system is:

Two bodies of $6 \,kg$ and $4 \,kg$ masses have their velocities $5 \hat{i}-2 \hat{j}+10 \hat{k}$ and $10 \hat{i}-2 \hat{j}+5 \hat{k}$ respectively. Then the velocity of their centre of mass is

$A$ man weighing $80\, kg$ is standing at the centre of a flat boat and he is $20\, m$ from the shore. He walks $8\, m$ on the boat towards the shore and then halts. The boat weighs $200\, kg$. How far is he from the shore at the end of this time?