Give an expression for the velocity and acceleration of the centre of mass of a system of particles.

Explanation

(i) `vecv=(dvecR)/(dt)=m_1(dvecr_i)/(dt)+m_2(dvecr_2)/(dt)+m_3(dvecr_3)/(dt)+……..+m_n(dvecr_n)/(dt)` where `v_1=(dvecr_1)/(dt),v_2=(dvecr_2)/(dt)`….. Represent velocities of mass particles `m_1,m_2,m_3`………. Etc.
(ii) `vecprop=(dvecv)/(dt)=m_1(dv_1)/(dt)+m_2(dv_2)/(dt)+........+m_x(dv_x)/(dt)`
where `veca_1=(dvecv_1)/(dt)," "veca_2=(dvecv^2)/(dt)`.............. represent acceleration of mass particles `m_1,m_2`..........