$(20$ points$)$ A point moves along along the coordinate line. It's displacement from $x=0$ is given by the function $s(t)$ below.

$]=[0$

Assume that the domain of $s(t)$ is $tt+-\sqrt[\phantom{2}]{\frac{2}{3}}(-,-\sqrt[\phantom{2}]{\frac{3}{3}})(\sqrt[\phantom{2}]{\frac{2}{3}},+)a(t)=6t$

$t=06(3)=18$ between mit

$6-30t2c,2^2$

$-5$

$2^3-2(2)+1$

$-4+1=5$

$t-2=5$

$t=8-so$ that $in$ this problem, $we$ allow for the time $ttobe$ negative. The units are not specified, $so$ you $do$ not need $to$ address such matters.

$(a)At$ which values $oftis$ the point $at$ rest?

$+-\sqrt[\phantom{2}]{\frac{2}{3}}At$ this point the slope $is0-$ theretore the point $isat$ rest

$(b)On$ which intervals $is$ the point moving $in$ a positive

$(-,-\sqrt[\phantom{2}]{\frac{3}{3}})(\sqrt[\phantom{2}]{\frac{2}{3}},+)$

$a(t)=6t$

$t=0$

$(c)On$ which intervals $is$ the point speeding $up?$

$6(3)=18$ between mit

$6-3$