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

Question

\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