Answer
a. $t=1.5$ sec.
b. $v\lt0$ during $0\leq t\lt 1.5$ sec, $v\gt0$ during $1.5\lt t\leq5$ sec,
c. $t=1.5$ sec.
d. $|v|$ increasing during $1.5\lt t\leq 5$ sec, $|v|$ decreasing during $0\leq t\lt 1.5$ sec,
e. $|v|=7$ at $t=5$ sec, $|v|=0$ at $t=1.5$ sec.
f. $12$ at $t=5$ sec.
Work Step by Step
Given $s(t)=t^2-3t+2$, $0\leq t\leq 5$, we have $v(t)=2t-3$, $a(t)=2$, and we can graph the functions as shown in the figure.
a. The object will be momentarily at rest when its velocity is zero. With $v(t)=0$, we have $t=1.5$ sec.
b. It moves left ($v\lt0$) during $0\leq t\lt 1.5$ sec, and it moves right ($v\gt0$) during $1.5\lt t\leq5$ sec,
c. It changes direction when its velocity crosses with the x-axis, so we have $t=1.5$ sec.
d. It speed up ($|v|$ increasing) during $1.5\lt t\leq 5$ sec, and it slows down ($|v|$ decreasing) during $0\leq t\lt 1.5$ sec,
e. It is moving fastest (highest speed $|v|=7$) at the end $t=5$ sec, and it is moving slowest ($|v|=0$) at $t=1.5$ sec.
f. It is farthest from the axis origin $12$ at $t=5$ sec.
