Overview
This lecture explains how to find the distance traveled from a velocity (or speed)–time graph by calculating the area under the graph, especially when speed changes.
Distance from Velocity/Speed–Time Graphs
- The formula distance = speed × time only works if speed is constant.
- When speed changes, use the area under the velocity or speed–time graph to find the distance traveled.
- For a section where the graph forms a triangle, calculate the area with ½ × base × height.
- Example: For a triangle with a base of 4 seconds and a height of 10 m/s, the area (distance) is ½ × 4 × 10 = 20 meters.
- Using only final speed × total time (e.g., 10 × 4 = 40 meters) is incorrect if speed is not constant.
- The area of a rectangle section of the graph is base × height.
- Example: Between 4 and 8 seconds (base = 4 s, height = 10 m/s), distance = 4 × 10 = 40 meters.
- Total distance in the first 8 seconds is the sum of both areas: 20 + 40 = 60 meters.
Key Terms & Definitions
- Velocity/Speed–Time Graph — A graph showing how speed or velocity changes over time.
- Area Under the Graph — Represents the distance traveled over a given time interval.
- Base — The length of the time interval on the graph.
- Height — The value of the speed or velocity at a given time.
Action Items / Next Steps
- Practice finding distance from velocity–time graphs using area calculations (triangles, rectangles).
- Review homework or textbook problems involving variable speed scenarios.