Answer
(a) $t=4sec$
(b) no time for $a=0$
(c) $(0,4)$
(d) $(4,8)$
Work Step by Step
(a) As $v=s'$, the velocity is equal to zero when $f(t)$ has a horizontal tangent line, which happens at $t=4sec$ as can be identified from the graph.
(b) As $a=s''$, the acceleration is equal to zero at the inflection points of the function $f(t)$. However, we can not identify any inflection points from the graph.
(c) The object moves forward when $s'=v\gt0$ and we can identify an interval of $(0,4)$ from the graph.
(d) The object moves backward when $s'=v\lt0$ and we can identify an interval of $(4,8)$ from the graph.
