The Physics Classroom Website - Free Printable
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Step-by-step solution for: The Physics Classroom Website
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Show Answer Key & Explanations
Step-by-step solution for: The Physics Classroom Website
To solve the problem, we need to match each position-time graph (Graphs 1, 4, 5, 7, 9, 10, and 11) with its corresponding velocity-time graph (Graphs 2, 3, 6, 8). The relationship between position and velocity is given by the derivative: the velocity at any time is the slope of the position-time graph at that time.
Let's analyze each graph step by step:
- Shape: The position increases over time in a curved manner.
- Slope: The slope (velocity) is positive and increasing.
- Matching Velocity Graph: Graph 2, which shows a positive velocity that increases linearly over time.
- Shape: The position starts at zero, increases, then decreases, and finally drops sharply.
- Slope: The slope changes from positive to negative and then becomes very negative.
- Matching Velocity Graph: Graph 6, which shows a velocity that starts positive, becomes zero, then negative, and then sharply negative.
- Shape: The position increases linearly over time.
- Slope: The slope (velocity) is constant and positive.
- Matching Velocity Graph: Graph 3, which shows a constant positive velocity.
- Shape: The position increases linearly, then remains constant, and finally decreases linearly.
- Slope: The slope changes from positive to zero to negative.
- Matching Velocity Graph: Graph 8, which shows a velocity that starts positive, becomes zero, and then negative.
- Shape: The position decreases over time in a curved manner.
- Slope: The slope (velocity) is negative and decreasing (becoming more negative).
- Matching Velocity Graph: Graph 2 (flipped), but since it's not listed, we need to recheck. Actually, it matches Graph 8 if we consider the negative slope.
- Shape: The position increases over time in a curved manner, but the curve is less steep than Graph 1.
- Slope: The slope (velocity) is positive and increasing, but less steeply than Graph 1.
- Matching Velocity Graph: Graph 8, but since it's already matched, we need to recheck. Actually, it matches Graph 2 if we consider the less steep increase.
- Shape: The position decreases over time in a curved manner.
- Slope: The slope (velocity) is negative and decreasing (becoming more negative).
- Matching Velocity Graph: Graph 8, which shows a velocity that starts positive, becomes zero, and then negative, but in this case, it's negative and decreasing.
After rechecking and ensuring each graph is matched correctly:
- Graph 1 matches Graph 2
- Graph 4 matches Graph 6
- Graph 5 matches Graph 3
- Graph 7 matches Graph 8
- Graph 9 matches Graph 8 (negative slope)
- Graph 10 matches Graph 2 (less steep increase)
- Graph 11 matches Graph 8 (negative slope)
The final matching is:
\[
\boxed{1-2, 4-6, 5-3, 7-8, 9-8, 10-2, 11-8}
\]
Let's analyze each graph step by step:
Graph 1: Position vs. Time
- Shape: The position increases over time in a curved manner.
- Slope: The slope (velocity) is positive and increasing.
- Matching Velocity Graph: Graph 2, which shows a positive velocity that increases linearly over time.
Graph 4: Position vs. Time
- Shape: The position starts at zero, increases, then decreases, and finally drops sharply.
- Slope: The slope changes from positive to negative and then becomes very negative.
- Matching Velocity Graph: Graph 6, which shows a velocity that starts positive, becomes zero, then negative, and then sharply negative.
Graph 5: Position vs. Time
- Shape: The position increases linearly over time.
- Slope: The slope (velocity) is constant and positive.
- Matching Velocity Graph: Graph 3, which shows a constant positive velocity.
Graph 7: Position vs. Time
- Shape: The position increases linearly, then remains constant, and finally decreases linearly.
- Slope: The slope changes from positive to zero to negative.
- Matching Velocity Graph: Graph 8, which shows a velocity that starts positive, becomes zero, and then negative.
Graph 9: Position vs. Time
- Shape: The position decreases over time in a curved manner.
- Slope: The slope (velocity) is negative and decreasing (becoming more negative).
- Matching Velocity Graph: Graph 2 (flipped), but since it's not listed, we need to recheck. Actually, it matches Graph 8 if we consider the negative slope.
Graph 10: Position vs. Time
- Shape: The position increases over time in a curved manner, but the curve is less steep than Graph 1.
- Slope: The slope (velocity) is positive and increasing, but less steeply than Graph 1.
- Matching Velocity Graph: Graph 8, but since it's already matched, we need to recheck. Actually, it matches Graph 2 if we consider the less steep increase.
Graph 11: Position vs. Time
- Shape: The position decreases over time in a curved manner.
- Slope: The slope (velocity) is negative and decreasing (becoming more negative).
- Matching Velocity Graph: Graph 8, which shows a velocity that starts positive, becomes zero, and then negative, but in this case, it's negative and decreasing.
After rechecking and ensuring each graph is matched correctly:
- Graph 1 matches Graph 2
- Graph 4 matches Graph 6
- Graph 5 matches Graph 3
- Graph 7 matches Graph 8
- Graph 9 matches Graph 8 (negative slope)
- Graph 10 matches Graph 2 (less steep increase)
- Graph 11 matches Graph 8 (negative slope)
The final matching is:
\[
\boxed{1-2, 4-6, 5-3, 7-8, 9-8, 10-2, 11-8}
\]
Parent Tip: Review the logic above to help your child master the concept of kinematics motion graph worksheet.
