Two particles are moving in the x$-$y plane. Particle #$1$ has a mass

m$1=8\mathrm{.}80$ kg

and is located $($at any time$)$ by the position vector

r$1($t$)=[0\mathrm{.}300$ m $+(2\mathrm{.}00$ m$/$s$2)$t$2]+0\mathrm{.}200$ m$.$

Particle #$2$ has a mass

m$2=4\mathrm{.}20$ kg

and is located $($at any time$)$ by the position vector

r$2($t$)=0\mathrm{.}100$ m$+[0\mathrm{.}300$ m $+(0\mathrm{.}500$ m$/$s$)$t $+(1\mathrm{.}50$ m$/$s$2)$t$2].$

Determine the following at the time

t $=1\mathrm{.}00$ s$.$

$($Express your answers in vector form.$)$

$($a$)$ location of the center of mass

rcm$($t $=1\mathrm{.}00$ s$)=$

Incorrect: Your answer is incorrect.

Review the definition for the location of the center of mass. m

$($b$)$ velocity of the center of mass

vcm$($t $=1\mathrm{.}00$ s$)=$

m$/$s

$($c$)$ acceleration of the center of mass

acm$($t $=1\mathrm{.}00$ s$)=$

Correct: Your answer is correct.

m$/$s$2$

$($d$)$ momentum of the center of mass

pcm$($t $=1\mathrm{.}00$ s$)=$

Incorrect: Your answer is incorrect.

How is the momentum of the center of mass related to the total mass of the system of particles and the velocity of the center of mass? kg $$ m$/$s

$($e$)$ net force acting on the center of mass

Fnet$($t $=1\mathrm{.}00$ s$)=$

N