Lesson Three: Graphing Motions
Lesson Three: Graphing Motions
Introduction
Objective: Understanding how graphs can depict changes in motion, specifically position and speed.
Materials: Graphing paper (optional), pencils, and ruler recommended for graphing activities.
Concept Connections
Graphs as tools for summarizing information.
Real-world analogies:
Hammer vs. screwdriver for driving nails: emphasizes using the right tools.
Key takeaway: Graphs summarize complex data succinctly.
Previous Lessons Recap
Key terms covered last week:
Velocity: A vector quantity with both speed and direction.
Acceleration: The rate of change of velocity.
Distance and Time: Associated concepts relevant to graphing motion.
Relation between distance, velocity, acceleration, and time.
Vocabulary
Slope: Defined in context of graphing as the steepness of a line.
Related to motion: a ski hill (incline) indicates slope.
Rise: Movement along the vertical axis; how high the line goes.
Run: Movement along the horizontal axis; how far the line goes.
Graphic Representation of Motion
Position Time Graph: Shows how an object's position changes with time.
Example: Graph depicting temperature changes in Santa Barbara, California on July 30, 2005.
Depicts fluctuations over time, similar to an object's changing position.
Creating a Position Time Graph
Data Collection:
Example scenario: Tracking the movement of a turtle with measurements taken every 20 seconds.
Table of Values:
Example entries (Time in seconds vs. Position in centimeters):
At 0s: 0cm
At 20s: 40cm
40s: 81cm
Will use the table to plot points.
Plotting Data:
X-axis: Time (seconds)
Y-axis: Position (centimeters)
Importance of using compatible scales for the axes.
Creating a Line of Best Fit:
Connecting plotted points to estimate unmeasured positions, such as at 19 seconds.
Graph Interpretation
Units: Position must be in consistent length units (e.g., centimeters, meters).
Example: What is the turtle's position at 70 seconds?
Using the graph to estimate the position: approximately 140 centimeters.
Comparing Two Objects' Motions
Turtle Race Graph:
Visual comparison of positions of two turtles plotted over the same timeframe.
Determining the winner based on who reaches 400cm first.
Interpretation of graphs can yield insights into each object’s movement.
Understanding Slope in Context of Motion
Slope represents average speed on a position time graph.
Steeper slopes indicate faster motion (e.g., colored line graph comparisons in example).
Calculating Slope:
Formula:
Using example values from the graph:
Determine rise and run from chosen points:
Example Points:
(0, 0) to (3, 60) results in:
Rise = 60 (y values), Run = 3 (x values).
Therefore, Slope = 60/3 = 20 meters/second.
Non-Linear Motion
Position-Time Graphs for Changing Speeds
Curve lines indicate changing speeds.
Characteristics:
Curved lines indicate acceleration or deceleration.
Example: Graph representing a train accelerating and then decelerating.
Speed-Time Graphs
Focuses on instantaneous speed.
Differences between position graphs and speed graphs:
Horizontal line in speed graph = constant speed.
Horizontal line in position graph = at rest.
Graph Types Summary
Position Time Graph: Shows object position over time; can be linear (constant speed) or nonlinear (changing speed).
Speed Time Graph: Displays an object’s speed, which can be constant or vary; horizontal line indicates constant speed, steep downward line indicates deceleration.
Application and Understanding
Every type of motion represented has distinct features in both graph types.
Developing skills to read, create and interpret motion graphs enhances understanding of physical principles.
Conclusion and Q&A
Open floor for questions regarding graph plotting, understanding slopes, and graph interpretation.