Overview
This lesson covers displacement-time graphs, focusing on interpreting movement, calculating speed and velocity, and understanding position in terms of displacement.
Displacement-Time Graph Basics
- Displacement is the object's position relative to a starting point (often a house or origin).
- Positive displacement is in a chosen direction (right, east, or north); negative is the opposite.
- When the graph is horizontal, the person/object is not moving.
- Returning to the starting point means displacement returns to zero.
Calculating Distance, Speed, & Velocity
- Total distance is always the sum of all traveled segments (ignore direction).
- Average speed = total distance / total time (scalar, m/s).
- Average velocity = change in displacement / change in time (vector, m/s, can be negative).
- For segments between two times, use starting and ending displacement and corresponding times.
Graph Interpretation Questions
- To find position at a given time, locate the time on the x-axis and read the displacement.
- If the graph declines, the subject is moving back toward or past the starting position (negative direction).
- If the graph is flat, no movement is occurring (velocity = 0).
Example Scenarios
- Walking from a house: right is positive; moving right increases displacement, left decreases.
- Cycling: east is positive; moving east increases displacement, returning or going west decreases it.
- Multiple stops: no movement during horizontal segments.
- Sprinting: direction chosen as positive; returning or reversing gives negative velocity.
Key Terms & Definitions
- Displacement — position relative to a starting point, can be positive or negative.
- Distance — total path length traveled, always positive (scalar).
- Speed — distance per unit time, scalar (m/s).
- Velocity — displacement per unit time, vector (m/s, includes direction).
- Average — calculated over a total time period, not instantaneous.
Action Items / Next Steps
- Practice interpreting and drawing displacement-time graphs.
- Solve example problems calculating distance, speed, and velocity.
- Review definitions and formulas for exam preparation.