Question

Three point masses of 2.0 kg each, have the following position vectors:

r^(t) =( t+ 4t²)miˆ + tmk^ ;
r2^(t) = 2t²mj^ -3 mk^ ;
r3^ = (t-1)mi^ + 4t²mj^

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

Answer 1

$$\hat{r}=\frac{1}{m+m+m}((( t+ 4t^2)m\hat{i} + tm\hat{k})+\\ (2t^2m\hat{j} -3 m\hat{k})+((t-1)m\hat{i}+ 4t^2m\hat{j}))$$

$$\hat{r}=\frac{1}{3}((4t^2+2t-1)\hat{i} + 6t^2\hat{j} +(t-3)\hat{k}))$$

The velocity of the centre of mass of the system

$$\hat{v}=\frac{1}{3}((8t+2)\hat{i} + 12t\hat{j} +\hat{k}))$$

The acceleration of the centre of mass of the system

$$\hat{a}=\frac{1}{3}(8\hat{i} + 12\hat{j} ))$$