Answer to Question #103319 in Physics for sakshi

Question

Three point masses of 2.0 kg each, have the following position vectors:
→ → →
r1(t)= (t+ 4t²)mi^ ; r2(t)= 2t²mj^-3mk^ ; r3
(t)= (t-1)mi^ +4t²mj^

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

Answer 1

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

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

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