Question

Three point masses of 3 kg each have the following position vectors:
r1 (t)= (2t+3t^2)mî+tmk
r2 (t)=4t^2mj+3mk
r3 (t)=(3t-1) mî+3t^2mj

Determine the velocity and acceleration of the centre of mass of the system.

Answer 1

r1 =  (2 t + 3 t²) m  i  + t m  k
r2  = (4 t² m  j + 3 m k
r3  =  (3 t -1)  m  i + 3 t² m j

Position vector of center of mass = [r1 + r2 + r3]/ 3
  r  = (3 t² + 5 t - 1) m  i + 7 t² m j + (3 + t) m k

velocity is =  dr /dt
       = (6 t + 5) m i  + 14 t m j + m k

acceleration = dv/dt =  6 m i + 14 m j