Question

which line segments show that the object is at rest? which line segments show the object is moving backwards? how long does it take the object to travel 10m? how fast is the object traveling during line segment #2?

Explanation:

Step1: Determine speed on line - segment 2

Speed is calculated as the slope of the position - time graph. For a position - time graph, the slope $m=\frac{\Delta x}{\Delta t}$. On line - segment 2, assume the initial position $x_1$, final position $x_2$, initial time $t_1$, and final time $t_2$. The slope gives the speed. However, since the question seems to be multiple - choice and we don't have specific data points for calculations, we can analyze the graph visually. A steeper slope means a higher speed.

Step2: Identify backward motion

On a position - time graph, if the position value is decreasing with time, the object is moving backwards. We look for line - segments where the $y$ - value (position) is getting smaller as the $x$ - value (time) is increasing.

Step3: Find time to travel 10m

We need to trace on the graph where the change in position $\Delta x = 10m$ and find the corresponding time interval.

Step4: Identify rest periods

On a position - time graph, when the object is at rest, the position does not change with time, so the graph is a horizontal line.

Answer:

1. For "How fast is the object traveling during line segment #2?": Need more data points on the graph to calculate the slope precisely. But visually, steeper slopes mean higher speeds.
2. For "Which line segments show the object is moving backwards?": We look for segments where position decreases with time.
3. For "How long does it take the object to travel 10m?": Trace on the graph for a $\Delta x=10m$ change in position and find the time interval.
4. For "Which line segments show that the object is at rest?": Horizontal line - segments on the position - time graph indicate the object is at rest. From the given answers, if 4 and 5 are horizontal segments, they show the object is at rest.