Question

practice it!
drag and drop the words or phrases that accurately label the graph.
distance (m)
time (s)
options: increasing speed, return to start, constant speed, decreasing speed, stationary

Explanation:

To solve this, we analyze the distance - time graph by looking at the slope (which represents speed, since \( \text{speed}=\frac{\text{change in distance}}{\text{change in time}} \)) of each segment:

Step 1: Analyze the first (top - most) segment

The curve here is concave and the slope (rate of change of distance with respect to time) is decreasing. A decreasing slope in a distance - time graph means that the speed is decreasing. So this segment is labeled "decreasing speed".

Step 2: Analyze the second (middle - straight) segment

A straight line in a distance - time graph has a constant slope. A constant slope implies a constant speed. So this segment is labeled "constant speed".

Step 3: Analyze the third (curved - upward) segment

The curve here is concave and the slope is increasing (as the curve gets steeper). An increasing slope in a distance - time graph means that the speed is increasing. So this segment is labeled "increasing speed".

Step 4: Analyze the fourth (vertical - like) segment

In a distance - time graph, if the distance does not change with time (a vertical line, or a line with infinite slope in the context of distance - time where time is on the y - axis and distance on the x - axis, but here time is on the y - axis and distance on the x - axis, so a vertical line would mean distance is constant as time changes), the object is not moving. So this segment is labeled "stationary".

Step 5: Analyze the fifth (bottom - straight) segment

The straight line here has a negative slope (since as time increases, distance decreases). A negative slope with a constant magnitude (straight line) means the object is moving back towards the start at a constant speed. So this segment is labeled "return to start" (with constant speed, but the key action is returning to start as distance is decreasing towards the initial position).

If we assume we are labeling from top to bottom of the graph segments:

1. Top segment: decreasing speed
2. Second segment: constant speed
3. Third segment: increasing speed
4. Fourth segment: stationary
5. Bottom segment: return to start

(The exact labeling depends on the order of the segments in the graph, but the above is the analysis of each type of segment based on distance - time graph principles)

Answer:

To solve this, we analyze the distance - time graph by looking at the slope (which represents speed, since \( \text{speed}=\frac{\text{change in distance}}{\text{change in time}} \)) of each segment:

Step 1: Analyze the first (top - most) segment

The curve here is concave and the slope (rate of change of distance with respect to time) is decreasing. A decreasing slope in a distance - time graph means that the speed is decreasing. So this segment is labeled "decreasing speed".

Step 2: Analyze the second (middle - straight) segment

A straight line in a distance - time graph has a constant slope. A constant slope implies a constant speed. So this segment is labeled "constant speed".

Step 3: Analyze the third (curved - upward) segment

The curve here is concave and the slope is increasing (as the curve gets steeper). An increasing slope in a distance - time graph means that the speed is increasing. So this segment is labeled "increasing speed".

Step 4: Analyze the fourth (vertical - like) segment

In a distance - time graph, if the distance does not change with time (a vertical line, or a line with infinite slope in the context of distance - time where time is on the y - axis and distance on the x - axis, but here time is on the y - axis and distance on the x - axis, so a vertical line would mean distance is constant as time changes), the object is not moving. So this segment is labeled "stationary".

Step 5: Analyze the fifth (bottom - straight) segment

The straight line here has a negative slope (since as time increases, distance decreases). A negative slope with a constant magnitude (straight line) means the object is moving back towards the start at a constant speed. So this segment is labeled "return to start" (with constant speed, but the key action is returning to start as distance is decreasing towards the initial position).

If we assume we are labeling from top to bottom of the graph segments:

1. Top segment: decreasing speed
2. Second segment: constant speed
3. Third segment: increasing speed
4. Fourth segment: stationary
5. Bottom segment: return to start

(The exact labeling depends on the order of the segments in the graph, but the above is the analysis of each type of segment based on distance - time graph principles)