Math Problem Statement
Solution
This problem involves calculating the average velocity over a specific time interval, using the provided position vs. time graph. Let’s analyze it step-by-step:
Problem Details:
- The graph shows the position (in meters) of an object moving along the -axis as a function of time (in seconds).
- The total displacement from to is shown.
- You are asked to calculate the average speed of the object during this interval.
Key Formula:
The average speed is calculated using:
Step 1: Analyze the graph
From the graph:
- The position starts at at .
- It reaches a maximum of at .
- Then it decreases back to at .
Step 2: Total distance traveled
The total distance is the sum of the segments:
- From to , the object moves from to . Distance = .
- From to , the object moves from back to . Distance = .
Thus, the total distance traveled is:
Step 3: Time interval
The total time interval is .
Step 4: Average speed calculation
Substitute the values into the formula for average speed:
Step 5: Check the options
The correct answer is .
Do you have any further questions or want details on the steps?
Here are 5 related questions to expand your understanding:
- How is total displacement different from total distance traveled?
- What is the difference between average speed and instantaneous speed?
- How would the solution change if the object started at instead of ?
- Can the average velocity ever be negative? Why or why not?
- How do we calculate the instantaneous velocity from a position-time graph?
Tip:
For position-time graphs, the slope at any point gives the instantaneous velocity, while the overall change in position divided by time gives the average velocity.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Average Velocity
Distance and Time
Formulas
v_avg = Total Distance / Time Interval
Theorems
The average velocity is the total distance traveled divided by the total time interval.
Suitable Grade Level
Grades 9-12
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