Question

when is the object at rest?
when is the object moving backwards?
when is the acceleration of the object positive?
what is the acceleration of the object from 11s - 13s?

Explanation:

Step1: Object at rest when v = 0

On the v - t graph, v = 0 at t = 0 s, t = 9 s and t = 13 s.

Step2: Object moving backwards when v<0

From the graph, v<0 in the interval 1 s - 9 s.

Step3: Acceleration positive when slope is positive

The slope of the v - t graph is positive in the intervals 9 s - 11 s and 1 s - 2 s.

Step4: Calculate acceleration from 11s - 13s

Acceleration $a=\frac{\Delta v}{\Delta t}$, $\Delta v=0 - 4=- 4$ m/s, $\Delta t=13 - 11 = 2$ s, so $a=\frac{-4}{2}=-2$ m/s².

Answer:

Object at rest: t = 0 s, t = 9 s, t = 13 s
Object moving backwards: 1 s - 9 s
Acceleration positive: 1 s - 2 s, 9 s - 11 s
Acceleration from 11s - 13s: - 2 m/s²