Answer
(a) moving away $(0,2),(6,9.5)~sec$, moving toward the origin $(2,6),(9.5,15)~sec$
(b) $t=2,6,9.5,15~sec$.
(c) $t=4,8,12.5~sec$.
(d) positive $(4,8),(12.5,15)~sec$, negative $(0,4),(8,12.5)~sec$.
Work Step by Step
On the given curve, we can estimate the velocity $v(t)=s'(t)$ and acceleration $a(t)=s''(t)$ as shown in the figure.
(a) As the displacement is always positive, the object is moving away from the origin when $v\gt0$ which gives time intervals of $(0,2),(6,9.5)~sec$, and is moving toward the origin when $v\lt0$ which gives time intervals of $(2,6),(9.5,15)~sec$
(b) The velocity is equal to zero when the curve reaches an extrema, which happens at times of $t=2,6,9.5,15~sec$.
(c) The acceleration is equal to zero at times when there is an inflection point, which gives $t=4,8,12.5~sec$.
(d) The acceleration is positive when the curve is concave up, which gives regions of $(4,8),(12.5,15)~sec$, The acceleration is negative when the curve is concave down which gives regions of $(0,4),(8,12.5)~sec$,
Please note the time may vary a little depending on the accuracy when reading the graph.
