This answer key provides solutions and explanations for a typical graphing motion worksheet. Since I don't have access to your specific worksheet, I will cover common question types encountered in these exercises. Remember to always refer to the specific instructions and variables used in your worksheet.
Understanding Position-Time Graphs
Key Concepts:
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Slope: The slope of a position-time graph represents velocity. A positive slope indicates positive velocity (movement in the positive direction), a negative slope indicates negative velocity (movement in the negative direction), and a zero slope indicates zero velocity (object at rest).
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Curvature: A curved line on a position-time graph indicates changing velocity (acceleration). A steeper curve means greater acceleration.
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Position: The y-axis represents the position of the object at any given time.
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Time: The x-axis represents the time elapsed.
Example Problems & Solutions:
Problem 1: A position-time graph shows a straight line with a positive slope. Describe the object's motion.
Solution: The object is moving with a constant positive velocity in the positive direction.
Problem 2: A position-time graph shows a horizontal line. Describe the object's motion.
Solution: The object is at rest; its position is not changing over time.
Problem 3: A position-time graph shows a straight line with a negative slope. Describe the object's motion.
Solution: The object is moving with a constant negative velocity in the negative direction.
Problem 4: A position-time graph shows a curved line that gets steeper over time. Describe the object's motion.
Solution: The object is accelerating in the positive direction; its velocity is increasing over time.
Problem 5: Calculate the velocity of an object from a position-time graph showing a straight line that passes through points (2s, 4m) and (6s, 12m).
Solution:
- Find the change in position (Δy): 12m - 4m = 8m
- Find the change in time (Δx): 6s - 2s = 4s
- Calculate the velocity (slope): Velocity = Δy/Δx = 8m/4s = 2 m/s
Understanding Velocity-Time Graphs
Key Concepts:
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Slope: The slope of a velocity-time graph represents acceleration. A positive slope means positive acceleration, a negative slope means negative acceleration (deceleration), and a zero slope means constant velocity (zero acceleration).
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Area Under the Curve: The area under the velocity-time curve represents the displacement of the object.
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Velocity: The y-axis represents the velocity of the object.
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Time: The x-axis represents the time elapsed.
Example Problems & Solutions:
Problem 6: A velocity-time graph shows a horizontal line. Describe the object's motion.
Solution: The object is moving with constant velocity (no acceleration).
Problem 7: A velocity-time graph shows a straight line with a positive slope. Describe the object's motion.
Solution: The object is accelerating at a constant rate in the positive direction.
Problem 8: A velocity-time graph shows a straight line with a negative slope. Describe the object's motion.
Solution: The object is decelerating (negative acceleration) at a constant rate.
Problem 9: Calculate the acceleration of an object from a velocity-time graph showing a straight line that passes through points (1s, 2m/s) and (5s, 10m/s).
Solution:
- Find the change in velocity (Δy): 10m/s - 2m/s = 8m/s
- Find the change in time (Δx): 5s - 1s = 4s
- Calculate the acceleration (slope): Acceleration = Δy/Δx = 8m/s / 4s = 2 m/s²
Remember to always carefully examine your specific worksheet for the exact questions and data points provided. Use the concepts outlined above to analyze the graphs and answer the questions accurately. If you have specific questions from your worksheet, feel free to provide them, and I will do my best to help you solve them.
