Position vs. Time Graphs - Physics | OpenStax

Section Learning Objectives

• Explain the meaning of slope in position vs. time graphs
• Solve problems using position vs. time graphs

Key Terms

• Dependent variable
• Independent variable
• Tangent

Graphing Position as a Function of Time

• Graphs illustrate relationships between physical quantities.
• Axes:
  • Horizontal axis: Independent variable (typically time)
  • Vertical axis: Dependent variable (typically position)
• Equation of Line:
  • General form: ( y = mx + b )
  • ( m ) is the slope (rise over run)
  • ( b ) is the y-intercept
• Slope and Intercepts in Physics:
  • Slope represents the average velocity.
  • y-intercept represents initial position.

Example Analysis

• Example: Drive to school
  • 5 km in 10 minutes at constant velocity.
  • Slope: Change in position over change in time (Average velocity)

Tips for Success

• Different time intervals may show different behaviors (series of straight lines).
• Calculate average velocity by analyzing slopes over each time interval.

Worked Example

• Jet-Powered Car on Salt Flats:
  • Uses position versus time to determine average velocity.
  • Slope of line on graph indicates velocity.
  • Example slope calculation from points: (6.4s, 2000m) and (0.5s, 525m)

Solving Problems Using Graphs

• Straight Line Graphs:
  • Easy to calculate average velocity (slope = rise/run)
• Curved Line Graphs:
  • Slope of tangent line at a point gives instantaneous velocity.
• Real-life Scenarios:
  • Position vs. time graphs can depict complex motion such as speeding up or changing direction.

Practice Problems

• Calculate average velocity or verify velocities using graph slopes.
• Assess understanding through questions related to motion interpretation from graphs.

Teacher Support

• Various methods demonstrated to help students visualize and interpret graphs.
• Practical demonstrations using simple tools like a toy car, meter stick, and stopwatch.

Snap Lab: Graphing Motion

• Activity involving rolling a ball down a ramp and graphing displacement vs. time.
• Encourages exploration of motion and data collection accuracy.

By understanding these concepts, students can effectively interpret and utilize position vs. time graphs in physics to analyze motion and calculate velocity.