Speed-time graphs are essential tools in physics for visualizing how an object's speed changes over time. Mastering these graphs is crucial for success in the Cambridge IGCSE Co-ordinated Sciences (0654) Physics syllabus.

1.1 What a Speed-Time Graph Represents

A speed-time graph plots an object's speed on the vertical (y) axis against time on the horizontal (x) axis. This standardized representation allows for consistent analysis of motion.

Key Points:

• X-axis (Horizontal): Time (in seconds, s)
• Y-axis (Vertical): Speed (in metres per second, m/s)
• SI Units: Always use m/s for speed, seconds for time, and metres for distance

Unit Conversion Reminder:

• 1 km/h = 0.2778 m/s
• 1 minute = 60 seconds

Different line shapes on a speed-time graph represent different types of motion:

Table 1: Interpreting Speed-Time Graph Shapes

The area under a speed-time graph represents the distance traveled by the object.

3.1 Conceptual Explanation

The relationship is based on the formula:

Distance = Speed × Time

When we calculate the area under a speed-time graph, we're essentially multiplying speed (y-axis) by time (x-axis), which gives us distance.

3.2 Geometric Interpretation

For IGCSE Physics, we typically deal with three shapes:

1. Rectangle: For constant speed
2. Triangle: For constant acceleration from rest
3. Trapezium: For constant acceleration with initial speed

4.1 Constant Speed (Rectangle)

Formula:

Distance = Speed × Time

Example:

A car travels at 15 m/s for 20 seconds.

• Distance = 15 m/s × 20 s = 300 m

4.2 Constant Acceleration from Rest (Triangle)

Formula:

Distance = ½ × Final Speed × Time

Example:

A car accelerates from rest to 20 m/s in 10 seconds.

• Distance = ½ × 20 m/s × 10 s = 100 m

4.3 Constant Acceleration with Initial Speed (Trapezium)

Formula:

Distance = ½ × (Initial Speed + Final Speed) × Time

Example:

A train accelerates from 10 m/s to 30 m/s over 50 seconds.

• Distance = ½ × (10 m/s + 30 m/s) × 50 s = 1000 m

For journeys involving multiple phases (acceleration, constant speed, deceleration), break the graph into sections and calculate each area separately.

5.1 Example: Multi-Stage Journey

A car's journey has three phases:

1. Phase A: Accelerates from rest to 10 m/s in 5 seconds (triangle)
2. Phase B: Travels at constant 10 m/s for 15 seconds (rectangle)
3. Phase C: Decelerates from 10 m/s to rest in 10 seconds (triangle)

Calculations:

1. Phase A: ½ × 10 m/s × 5 s = 25 m
2. Phase B: 10 m/s × 15 s = 150 m
3. Phase C: ½ × 10 m/s × 10 s = 50 m

Total Distance = 25 m + 150 m + 50 m = 225 m

Common Errors:

• Forgetting to convert units (e.g., km/h to m/s)
• Confusing speed-time with distance-time graphs
• Misidentifying the shape of the graph section
• Incorrectly calculating areas of triangles and trapeziums

Examination Tips:

1. Always label axes with quantities and units
2. Show all working clearly
3. Use the correct formula for each shape
4. Check that units are consistent
5. Estimate answers to check reasonableness

• Gradient of speed-time graph = Acceleration
• Area under speed-time graph = Distance traveled
• Horizontal line = Constant speed (zero acceleration)
• Straight sloping line = Constant acceleration
• Curved line = Changing acceleration

By understanding these principles and practicing with various examples, you'll be well-prepared to tackle any speed-time graph problem in your IGCSE Physics exam.