Question

think about the process the graph shows the speed of your neighbors car on her way back home last friday. you want to find the number of constant intervals defined in the graph. what should be your first step? how many constant intervals are defined in the graph? what should be your first step? a. identify the lines that have negative slope. b. identify the lines that have positive slope. c. identify the lines that have a slope of zero. how many constant intervals are defined in the graph?

Explanation:

Step1: Analyze constant intervals

A constant interval in a speed - time graph is where the speed does not change, which corresponds to a line segment with a slope of zero (horizontal line). So first, we identify the line segments with slope zero.
Looking at the graph:
- The first constant interval: After the initial increase, there is a horizontal line (slope = 0) around 4:00 - 4:30? Wait, no, let's re - examine. Wait, the graph has:
- First, a rising line (positive slope), then a horizontal line (slope = 0), then a drop to zero, then a rising line, then a horizontal line, then a drop, then a horizontal line, then a drop? Wait, no, let's count the horizontal segments (slope = 0):
- The first horizontal segment (constant speed) after the first increase.
- Then after the second increase, there is a horizontal segment.
- Then after a drop, there is another horizontal segment.
Wait, let's look at the graph coordinates. The time is from 4:00 to 6:30. The speed - time graph:
- From 4:00 to around 4:15 (approx) rising, then a horizontal line (constant speed) until maybe 4:30? Then a drop to 0. Then a rise to a higher speed, then a horizontal line (constant speed) from around 5:00 to 5:30? Then a drop, then a horizontal line (constant speed) for a short time, then a drop to zero. Wait, no, let's count the number of horizontal (slope = 0) segments:
1. The first horizontal segment (after the first rise).
2. The second horizontal segment (after the second rise).
3. The third horizontal segment (after the first drop from the second horizontal segment).

Wait, actually, looking at the graph, the constant intervals (where speed is constant, i.e., slope = 0) are:
- The first one: when the speed is constant (horizontal line) after the first increase.
- The second one: when the speed is constant (horizontal line) after the second increase.
- The third one: when the speed is constant (horizontal line) after the first drop from the second constant interval.

Wait, let's count again. Let's see the graph:

- Segment 1: Rising (positive slope)
- Segment 2: Horizontal (slope = 0, constant speed)
- Segment 3: Falling (negative slope) to 0
- Segment 4: Rising (positive slope)
- Segment 5: Horizontal (slope = 0, constant speed)
- Segment 6: Falling (negative slope)
- Segment 7: Horizontal (slope = 0, constant speed)
- Segment 8: Falling (negative slope) to 0

Wait, no, maybe I mis - see. Let's look at the y - axis (speed) and x - axis (time). The key is that a constant interval is a horizontal line. So the number of horizontal lines (slope = 0) is 3? Wait, no, let's check the options for the first part: the first step is to identify lines with slope 0 (option C). Then for the number of constant intervals:

Looking at the graph, we can see three horizontal segments (where speed is constant, slope = 0). Wait, let's count:

1. The first horizontal segment (after the first increase in speed).
2. The second horizontal segment (after the second increase in speed).
3. The third horizontal segment (after a decrease in speed, before the final decrease).

So the number of constant intervals is 3.

Step1 (for the first question):

To find the number of constant intervals in a speed - time graph, a constant interval occurs when the speed does not change, which is represented by a line segment with a slope of 0 (horizontal line). So the first step is to identify the lines that have a slope of zero (option C).

Step2 (for the second question):

We count the number of horizontal (slope = 0) segments in the speed - time graph. By visually inspecting the graph, we can see that there are 3 such segments (constant intervals).

Answer:

For the first question: C. Identify the lines that have a slope of zero.
For the second question: 3