Overview
The lesson covers how to interpret displacement-time graphs, analyze motion using these graphs, and calculate distance, speed, and velocity for various movement scenarios.
Understanding Displacement-Time Graphs
- Displacement-time graphs show an object's position relative to a starting point over time.
- Positive displacement values indicate movement in the chosen positive direction (e.g., right, east, or north).
- Negative displacement shows movement in the opposite (negative) direction.
- Flat (horizontal) segments on a displacement-time graph mean the object is not moving.
Key Examples and Calculations
Example 1: Walking from Home
- The person walks 4 meters right, returns to the house, then goes 4 meters left (negative).
- Total distance walked: 4 m (right) + 8 m (to -4 left) = 12 meters.
- Average speed: 12 m / 15 s = 0.8 m/s.
- At 10 and 15 seconds, the person is 4 meters left of the house.
- Between 10-15 seconds, the person is stationary.
- Velocity (5-10 s): (-4 - 4) / (10 - 5) = -1.6 m/s (left).
Example 2: Cycling East and West
- Moves 60 meters east, stops, returns home, then 40 meters west, then back home.
- Total distance: 60 + 60 + 40 + 40 = 200 meters.
- Average speed: 200 m / 55 s = 3.64 m/s.
- At 30 s: back at starting position (0 meters).
- At 35 s: 20 meters west of the house.
- Velocity (15-40 s): (-40 - 60) / (40 - 15) = -4 m/s (west).
Example 3: Sarah Walking North and South
- Goes 2 m north, pauses, returns to start, goes 1 m south, pauses, returns to start.
- Total distance: 2 + 2 + 1 + 1 = 6 meters.
- At 7 s: 1 meter south of starting point.
- Velocity (0-2 s): (2 - 0) / (2 - 0) = 1 m/s north.
- Velocity (4-6 s): (-1 - 2) / (6 - 4) = -1.5 m/s south.
- Velocity (6-8 s): (-1 - -1) / (8 - 6) = 0 m/s.
Example 4: Greg Sprinting West/East
- Sprints 8 m west, stops, returns to start, 8 m east, stops, returns to start.
- Velocity (0-2 s): (8 - 0) / (2 - 0) = 4 m/s west.
- Velocity (4-8 s): (-8 - 8) / (8 - 4) = -4 m/s (4 m/s east).
- Velocity (8-10 s): (-8 - -8) / (10 - 8) = 0 m/s.
Example 5: Boat Moving East and West
- Moves 40 m east, pauses, goes to -40 m west, then to 20 m east, pauses, returns to start.
- Velocity (30-50 s): (-40 - 40) / (50 - 30) = -4 m/s (west).
- Velocity (0-30 s): (40 - 0) / (30 - 0) = 1.33 m/s east.
- From G to H, boat is stationary (not moving).
- Total distance: 40 + 80 + 60 + 20 = 200 meters.
Key Terms & Definitions
- Displacement — Change in position from the starting point, including direction (vector).
- Distance — Total length of the path traveled, regardless of direction (scalar).
- Speed — Distance traveled divided by time taken (scalar), (\text{speed} = \frac{\text{distance}}{\text{time}}).
- Velocity — Displacement divided by time taken (vector), (\text{velocity} = \frac{\Delta \text{displacement}}{\Delta \text{time}}).
- Stationary — No change in displacement over time; object is not moving.
Action Items / Next Steps
- Practice drawing and interpreting displacement-time graphs for various movements.
- Solve additional problems calculating distance, speed, and velocity from different graphs.
- Review the definitions and differences between distance/displacement and speed/velocity.
- Complete any assigned homework or reading on motion and graphs as instructed.