Overview
This lecture explains how to interpret distance-time graphs, focusing on understanding speed, constant and changing motion, and how to calculate speed at different stages.
Understanding Distance-Time Graphs
- Distance-time graphs show how far something has traveled over a period.
- The gradient (slope) of the line at any point gives the object's speed at that moment.
- Gradient is calculated as change in distance divided by change in time (which is the formula for speed).
- A straight, sloped line indicates constant speed.
- A flat (horizontal) line means the object is stationary (speed is zero).
- A line that becomes steeper signifies increasing speed (acceleration).
- A line with decreasing steepness shows slowing down (deceleration).
Calculating Speed from the Graph
- For straight sections, calculate speed by dividing total distance by total time for that segment.
- For example, traveling 20 meters in 2 seconds: speed = 20 ÷ 2 = 10 m/s (constant speed).
- For curved sections, draw a tangent at the desired point to estimate the speed.
- Calculate the gradient of the tangent by dividing the change in distance by the change in time between two points on the tangent.
- Example: If tangent rises 12 meters in 3 seconds, speed = 12 ÷ 3 = 4 m/s.
Summary of Graph Features
- Straight lines = constant speed.
- Flat lines = stationary (no movement).
- Curved lines = changing speed.
- Use gradient (or tangent's gradient for curves) to find speed at any point.
Key Terms & Definitions
- Distance-time graph — a graph showing how distance changes over time.
- Gradient — the slope of the line, indicating speed.
- Speed — distance traveled divided by time taken.
- Tangent — a straight line that touches a curve at one point and matches its gradient there.
- Stationary — not moving; speed is zero.
Action Items / Next Steps
- Practice interpreting distance-time graphs and calculating speed for both straight and curved sections.