Math Problem Statement
can you help me solve part b
Solution
To help you with part b, I'll first analyze the content of the image.
Analysis:
- The image shows a velocity vs. time graph of an object's motion.
- Part b asks, "How much distance does the car cover in the first 8 seconds?"
Steps to solve:
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Understand the problem:
- The distance covered by the car can be found by calculating the area under the velocity vs. time graph. This is because the area under the curve in a velocity-time graph represents the displacement (distance traveled in a straight line) of the object.
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Divide the area into shapes:
- The graph can be divided into rectangular and triangular areas.
- You need to calculate the area of each shape from 0 to 8 seconds and then sum these areas to find the total distance.
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Calculate the area:
- For each rectangular section: Area = width × height.
- For any triangular section (if applicable): Area = 0.5 × base × height.
Calculation:
Based on the graph:
- From 0 to 2 seconds, the velocity is 3 m/s (rectangle).
- From 2 to 4 seconds, the velocity is -3 m/s (rectangle).
- From 4 to 6 seconds, the velocity is 2 m/s (rectangle).
- From 6 to 8 seconds, the velocity is -2 m/s (rectangle).
Now, let's compute the area:
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0 to 2 seconds:
-
2 to 4 seconds:
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4 to 6 seconds:
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6 to 8 seconds:
Sum of all areas:
Conclusion:
- The distance covered by the car in the first 8 seconds is 0 meters. This indicates that the car returns to its original position.
Would you like any further details, or do you have additional questions?
Relative Questions:
- How would the answer change if the graph was not symmetric?
- What does the negative area under the curve represent in real-life scenarios?
- How would you find the total distance if there was an acceleration involved?
- What if the time intervals weren't uniform? How would that affect the calculation?
- How does the concept of distance differ from displacement in this context?
Tip:
When analyzing motion graphs, always distinguish between distance (the total path covered) and displacement (the change in position).
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Math Problem Analysis
Mathematical Concepts
Physics
Kinematics
Area under Velocity-Time Graph
Formulas
Area calculation for velocity-time graph
Theorems
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Suitable Grade Level
High School
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