The vector position of a $3\mathrm{.}50-g$ particle moving in the $xy$ plane varies in time according to vec$(r{)}_1=(3$hat$(i)+3$hat$(j))t+2$hat$(j){}^2,$ where $t$ is in seconds and vec$(r)$ is in centimeters. At the same time, the vector position of a $5\mathrm{.}50$ g particle varies as vec$(r{)}_2=3$hat$(i)-2$hat$(i)t^2-6$hat$(j)t.$ At $t=2\mathrm{.}50s,$ 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.