Graphs in Practical Situations

2.9 Graphs in Practical Situations – Cheat Sheet

1. Types of Practical Graphs

2. Interpreting Travel (Distance–Time) Graphs

• Gradient = speed
• Flat section = stationary
• Steeper gradient = faster speed
• Negative gradient = returning to starting point

Example:
If gradient = 100 m / 20 s → speed = 5 m/s

3. Interpreting Conversion Graphs

• Usually straight lines → direct proportion.
• Read values by finding the given unit on one axis and reading the corresponding value on the other.

Example:
1 mile = 1.6 km → conversion graph slope = 1.6

4. Interpreting Speed–Time Graphs

5. Rate of Change

• Gradient = rate of change in distance–time and speed–time graphs.
• Acceleration = gradient of speed–time graph.
• Speed = gradient of distance–time graph.

Example:
Speed–Time: speed changes from 10 m/s to 20 m/s in 5 s → acceleration = (20 − 10) / 5 = 2 m/s²

6. Distance Travelled from Speed–Time Graph

• Distance = area under the speed–time graph.
• For rectangles: area = base × height.
• For triangles: area = ½ × base × height.
• For combined shapes, add areas.

Example:
Triangle: base = 4 s, height = 8 m/s → distance = ½ × 4 × 8 = 16 m

7. Estimating Gradient of a Tangent

• Draw a tangent at the given point.
• Gradient = vertical change / horizontal change.

Example:
Tangent rise = 6 m, run = 2 s → gradient = 6 / 2 = 3 m/s

8. Examples Table for Quick Reference