Question

The graph below depicts an object's distance traveled over several intervals of time.

\begin{tikzpicture}[scale=0.8]
\draw[<->] (0,0) -- (5,0) node[right] {Time};
\draw[<->] (0,0) -- (0,3) node[above] {Distance};
\draw (0,0) node[below left] {A};
\draw (1,0) node[below] {B};
\draw (2,2) node[above] {C};
\draw (3,2) node[above] {D};
\draw (4,2.5) node[above] {E};
\draw[thick] (1,0) -- (2,2) -- (3,2) to[out=0,in=180] (4,2.5);
\end{tikzpicture}

Which option correctly lists the motion of the object for each time interval?
(1 point)
interval AB → no motion
interval BC → constant speed
interval CD → no motion
interval DE → acceleration

interval AB → no motion
interval BC → decreasing speed
interval CD → constant speed
interval DE → acceleration

interval AB → constant speed
interval BC → decreasing speed
interval CD → constant speed
interval DE → increasing speed

interval AB → constant speed
interval BC → acceleration
interval CD → constant speed
interval DE → acceleration

Answer 1

To analyze the motion of the object in each interval represented by the graph, let's evaluate the characteristics of the distance vs. time graph.

1. **Interval AB**: The line goes from (0,0) to (1,0) which indicates that the distance remains at 0. Therefore, the object is **not moving** during this interval.

2. **Interval BC**: The line rises from (1,0) to (2,2) indicating that the distance is increasing steadily. Since the slope is constant, this means the object is traveling at a **constant speed** during this interval.

3. **Interval CD**: The line stays horizontal at a distance of 2 between points (2,2) and (3,2). This indicates that the object is at rest, hence there is **no motion** during this interval.

4. **Interval DE**: The line rises from (3,2) to (4,2.5). Since the distance is increasing and the slope is positive, this indicates that the object is experiencing **acceleration** as it travels.

Given this analysis, the correct option that describes the motion of the object for each time interval is:

**Interval AB → no motion
Interval BC → constant speed
Interval CD → no motion
Interval DE → acceleration**