Serway & Jewett — Linear Momentum and Collisions: Problem 28

The vector position of a 3.50-g particle moving in the $xy$ plane varies in time according to $\vec{r}_1 = (3\hat{i} + 3\hat{j})t + 2\hat{j}t^2$, where $t$ is in seconds and $\vec{r}$ is in centimeters. At the same time, the vector position of a 5.50 g particle varies as $\vec{r}_2 = 3\hat{i} - 2\hat{i}t^2 - 6\hat{j}t$. At $t = 2.50\text{ s}$, determine (a) the vector position of the center of mass of the system, (b) the linear momentum of the system, (c) the velocity of the center of mass, (d) the acceleration of the center of mass, and (e) the net force exerted on the two-particle system.