This answer key provides solutions and explanations for a typical graphing motion worksheet. Since I don't have access to your specific worksheet, I'll cover common question types encountered when interpreting position-time and velocity-time graphs. Remember to always check your specific worksheet for units and any special instructions.
Understanding Position-Time Graphs
Position-time graphs illustrate an object's position (distance from a reference point) at different points in time.
Key Features:
- Slope: The slope of a position-time graph represents the object's velocity.
- A positive slope indicates positive velocity (movement in the positive direction).
- A negative slope indicates negative velocity (movement in the negative direction).
- A zero slope indicates zero velocity (the object is stationary).
- Y-intercept: The y-intercept represents the object's initial position at time t=0.
Example Question:
A position-time graph shows a straight line with a positive slope. Describe the object's motion.
Answer: The object is moving with a constant positive velocity in the positive direction.
Understanding Velocity-Time Graphs
Velocity-time graphs show an object's velocity at different points in time.
Key Features:
- Slope: The slope of a velocity-time graph represents the object's acceleration.
- A positive slope indicates positive acceleration (increasing velocity).
- A negative slope indicates negative acceleration (decreasing velocity or deceleration).
- A zero slope indicates constant velocity (no acceleration).
- Area Under the Curve: The area under the velocity-time graph represents the object's displacement. Remember to consider the sign (positive or negative) of the area.
- Y-intercept: The y-intercept represents the object's initial velocity at time t=0.
Example Question:
A velocity-time graph shows a horizontal line at v = 5 m/s. Describe the object's motion.
Answer: The object is moving with a constant velocity of 5 m/s; its acceleration is zero.
Common Graphing Motion Worksheet Problems:
Here are examples of common problem types found in graphing motion worksheets, along with how to approach them:
1. Determining Velocity from a Position-Time Graph:
Calculate the velocity of an object given a position-time graph showing points (2s, 4m) and (6s, 12m).
- Solution: Velocity = (change in position) / (change in time) = (12m - 4m) / (6s - 2s) = 2 m/s
2. Determining Acceleration from a Velocity-Time Graph:
Calculate the acceleration of an object given a velocity-time graph showing points (1s, 2m/s) and (4s, 8m/s).
- Solution: Acceleration = (change in velocity) / (change in time) = (8m/s - 2m/s) / (4s - 1s) = 2 m/s²
3. Determining Displacement from a Velocity-Time Graph:
Find the displacement of an object from a velocity-time graph showing a rectangle with a base of 5s and a height of 3m/s.
- Solution: Displacement = area under the curve = base × height = 5s × 3m/s = 15m
4. Interpreting Complex Graphs:
Graphs might include sections with different slopes or curves, representing changes in velocity or acceleration. Carefully analyze each section separately to describe the motion accurately. Remember to consider both magnitude and direction.
Remember: Always carefully read the axes labels on your graphs to understand the units and variables being represented. Accurate interpretation of these labels is crucial for solving problems correctly. If your worksheet includes specific scenarios or more complex graphs, provide them, and I'll assist you further.
