Answer
(a) $t=0,6,12sec$
(b) $t=3,9sec$
(c) $(6,12)$
(d) $(0,6)$ and $(12,14)$
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 $t=0,6,12sec$ as can be identified from the graph.
(b) As $a=s''$, the acceleration equal to zero at the inflection points of the function $f(t)$. Based on concavity changes, we can identify the inflection points at $t=3,9sec$ as can be identified from the graph.
(c) The object moves forward when $s'=v\gt0$ and we can identify an interval of $(6,12)$ from the graph.
(d) The object moves backward when $s'=v\lt0$ and we can identify intervals of $(0,6)$ and $(12,14)$ from the graph.
