Overview
This lecture explains the concepts of speed and velocity, illustrates how to plot motion on a distance-time graph, and introduces the idea of slope as a representation of speed.
Speed and Its Calculation
- Speed is defined as the distance traveled divided by the time taken.
- In the example, the car travels 100 m in 5 seconds, so speed = 100 m / 5 s = 20 m/s.
- Speed tells how much distance an object covers every second.
- Common units for speed include meters per second (m/s) and miles per hour (mph).
- If speed varies during the journey, the calculated value represents average speed.
Distance-Time Graphs
- Motion can be represented on paper using a distance-time graph, with time on the horizontal axis and distance on the vertical axis.
- Points on the graph correspond to the distance traveled at each second: (0,0), (1,20), (2,40), (3,60), (4,80), (5,100).
- Connecting these points forms a straight line, indicating constant speed.
Interpreting the Graph: Slope and Speed
- The slope of the distance-time graph (vertical change/horizontal change) equals speed.
- Slope can be calculated as change in y (distance) divided by change in x (time).
- A steeper slope means greater speed; a flatter slope means less speed.
- A horizontal line (zero slope) shows the object is at rest (speed = 0).
Velocity and Its Difference from Speed
- Velocity is speed with a specified direction.
- For example, 20 m/s to the right is velocity, while 20 m/s is just speed.
- Velocity includes both magnitude (how fast) and direction (which way).
Key Terms & Definitions
- Speed — Distance traveled divided by time taken (unit: m/s).
- Average Speed — Total distance divided by total time, used when speed varies.
- Distance-Time Graph — A plot with time on the x-axis and distance on the y-axis.
- Slope — The rise over run (vertical/horizontal change) of a graph, representing speed on a distance-time graph.
- Velocity — Speed in a given direction.
Action Items / Next Steps
- Practice calculating speed and plotting distance-time graphs for different scenarios.
- Review the difference between speed and velocity with more examples.