Question
The function shown below was created to track the different intervals of speed that an automobile travels over a period of 28 seconds.
Use the graph of the function to complete Parts 1-3.
After traveling for 16 seconds, the automobile begins to slow its speed at a steady rate. Use the coordinates on the graph to determine the rate at which the car is slowing down, in miles per hour per second.
During which interval of time does the automobile experience the greatest change in its speed? What is the change in the automobile's speed during this interval?
For a time period of approximately 10 seconds, the automobile experiences no change in its speed. During which interval of time does the automobile's speed remain constant? At what speed is the automobile traveling during this interval?
WRITER
Use the graph of the function to complete Parts 1-3.
After traveling for 16 seconds, the automobile begins to slow its speed at a steady rate. Use the coordinates on the graph to determine the rate at which the car is slowing down, in miles per hour per second.
During which interval of time does the automobile experience the greatest change in its speed? What is the change in the automobile's speed during this interval?
For a time period of approximately 10 seconds, the automobile experiences no change in its speed. During which interval of time does the automobile's speed remain constant? At what speed is the automobile traveling during this interval?
WRITER
Answers
GPT-4o mini
To answer the questions regarding the function that tracks the speed of the automobile over 28 seconds, we can break down the requirements based on the information given about the graph of the speed function.
### Part 1: Rate of Deceleration
To determine the rate at which the car is slowing down after 16 seconds, we need to find the speed at 16 seconds and at the time when it stops decelerating. Let's assume the speeds (in miles per hour) at 16 seconds and 28 seconds are available from the graph.
1. Speed at 16 seconds: Let’s call this \( S_{16} \).
2. Speed at 28 seconds: Let’s call this \( S_{28} \).
3. The time interval for deceleration is from 16 seconds to 28 seconds, which is 12 seconds.
To find the rate of deceleration in miles per hour per second, we use the formula:
\[
\text{Rate of Deceleration} = \frac{S_{28} - S_{16}}{28 - 16} \text{ mph/s}
\]
### Part 2: Greatest Change in Speed
To find the interval during which the automobile experiences the greatest change in speed, we need to look for the steepest changes on the graph. This will typically be the interval where the graph is either increasing or decreasing most sharply (i.e., the highest slope).
1. Identify the highest increase or decrease in speed on the graph between two points in time.
2. Calculate the change in speed:
\[
\text{Change in Speed} = \text{Speed at higher time} - \text{Speed at lower time}
\]
### Part 3: Constant Speed Interval
To find the interval where the speed remains constant, we look for flat horizontal segments in the graph.
1. Identify the time period where the speed does not change (graph is horizontal).
2. Note down the speed during this interval from the graph.
This speed would be the same throughout the constant interval.
### Conclusion
To finalize the answers, you would need specific data points from the graph (like coordinates) for calculations. If you can provide the values from the graph, I can assist you with calculating the exact answers for each part!
### Part 1: Rate of Deceleration
To determine the rate at which the car is slowing down after 16 seconds, we need to find the speed at 16 seconds and at the time when it stops decelerating. Let's assume the speeds (in miles per hour) at 16 seconds and 28 seconds are available from the graph.
1. Speed at 16 seconds: Let’s call this \( S_{16} \).
2. Speed at 28 seconds: Let’s call this \( S_{28} \).
3. The time interval for deceleration is from 16 seconds to 28 seconds, which is 12 seconds.
To find the rate of deceleration in miles per hour per second, we use the formula:
\[
\text{Rate of Deceleration} = \frac{S_{28} - S_{16}}{28 - 16} \text{ mph/s}
\]
### Part 2: Greatest Change in Speed
To find the interval during which the automobile experiences the greatest change in speed, we need to look for the steepest changes on the graph. This will typically be the interval where the graph is either increasing or decreasing most sharply (i.e., the highest slope).
1. Identify the highest increase or decrease in speed on the graph between two points in time.
2. Calculate the change in speed:
\[
\text{Change in Speed} = \text{Speed at higher time} - \text{Speed at lower time}
\]
### Part 3: Constant Speed Interval
To find the interval where the speed remains constant, we look for flat horizontal segments in the graph.
1. Identify the time period where the speed does not change (graph is horizontal).
2. Note down the speed during this interval from the graph.
This speed would be the same throughout the constant interval.
### Conclusion
To finalize the answers, you would need specific data points from the graph (like coordinates) for calculations. If you can provide the values from the graph, I can assist you with calculating the exact answers for each part!