Acceleration & Speed-Time Graphs
IGCSE Physics 1.2.4-1.2.9 (Core & Supplement)
🚗 The Hook: The Gas Pedal
Ever notice how your body pushes back into the car seat when the driver steps on the gas? That feeling is acceleration - the change in speed over time. A racing car accelerates from 0 to 100 km/h in just 3 seconds, while a bicycle might take 30 seconds. The difference? The rate of change of velocity.
🎯 Why Learn This?
Pilots calculate acceleration for takeoff distances. Engineers design braking systems to stop cars safely. Understanding acceleration graphs helps predict motion, design vehicles, and analyze crashes. This skill is tested in Paper 2 (MCQs), Paper 4 (Calculations), and Paper 6 (Graph Analysis).
📚 Baby Steps: What is Acceleration?
Imagine you're in a car. The speedometer shows 20 m/s. Three seconds later, it shows 50 m/s. Your speed changed by 30 m/s in 3 seconds. That's acceleration - how quickly your velocity changes.
In plain English: Acceleration tells you how much faster (or slower) something gets every second.
- ✓If a car goes from 10 m/s to 30 m/s in 5 seconds, it accelerates by 4 m/s every second.
- ✓If a bicycle slows from 15 m/s to 5 m/s in 2 seconds, it has negative acceleration (deceleration).
- ✓If a train maintains 60 m/s for 10 seconds, its acceleration is zero (constant speed).
🎮 Interactive Simulator: The Gas Pedal Dashboard
📐 Visual Clarification: Speed-Time Graphs
A speed-time graph is the most powerful tool for understanding acceleration. Let's break down what different parts of the graph mean.
Gradient = Acceleration
Speeding up (0-2s)
Gradient = 0 (No acceleration)
Constant speed (2-5s)
Negative gradient = Deceleration
Slowing down (5-8s)
🎯 Interactive Tool: The Area Under the Graph
Here's a critical IGCSE concept: The area under a speed-time graph equals the distance travelled.
📏 Area Calculation:
This triangle represents a car accelerating from 0 to 20 m/s over 8 seconds.
Area = ½ × base × height = ½ × 8s × 20m/s = 80 meters
The car travelled 80 meters during this acceleration period!
🔬 Deep Theory: Mark Scheme Keywords
⚙️ Core Content
1. Distance-Time vs Speed-Time Graphs
Distance-Time Graph
Gradient = Speed
Flat line = Stationary (at rest)
Straight line = Constant speed
Speed-Time Graph
Gradient = Acceleration
Flat line = Constant speed
Area under = Distance travelled
2. Calculating Distance from Speed-Time Graph
For motion with constant speed or constant acceleration:
Distance = Area under the graph
Rectangle (constant speed): Distance = speed × time
Triangle (constant acceleration): Distance = ½ × (final speed + initial speed) × time
3. Free Fall Acceleration
g = acceleration of free fall (also called gravitational field strength)
g ≈ 9.8 m/s² (or approximately 10 m/s²)
This means all objects near Earth's surface accelerate downward at ~10 m/s² when falling freely (ignoring air resistance).
🎓 Supplement Content
1. Definition of Acceleration (CRITICAL)
Mark Scheme Keyword:
"Acceleration is the change in velocity per unit time"
Formula: a = Δv / Δt
where Δv = change in velocity (v - u)
and Δt = time taken
2. Calculating Acceleration from Speed-Time Graph
Gradient of speed-time graph = Acceleration
Acceleration = (change in speed) / (time taken) = Δv / Δt
3. Deceleration
Deceleration is negative acceleration
When an object slows down, the acceleration value is negative. Use this in calculations.
Example: If a car slows from 20 m/s to 5 m/s in 3s, a = (5-20)/3 = -5 m/s²
4. Constant vs Changing Acceleration
Constant acceleration: Straight line on speed-time graph
Changing acceleration: Curved line on speed-time graph
5. Terminal Velocity (Free Fall)
When an object falls through air or liquid:
• Initially: Accelerates at g (9.8 m/s²)
• Air resistance increases with speed
• Terminal velocity: When air resistance = weight, acceleration becomes zero
• Object continues falling at constant maximum speed
🔬 Virtual Lab: Free Fall Timer
Let's simulate an object falling under gravity. Watch how velocity increases by approximately 10 m/s every second.
📊 Calculations
Acceleration (g): 10 m/s²
Time: 0.0 s
Final Velocity: v = g × t = 10 × 0.0 = 0.0 m/s
Distance Fallen: s = ½gt² = ½ × 10 × 0.0² = 0.0 m
🎮 Graph Shape Sorter: The Examiner's Trap!
CRITICAL TRAP: A horizontal line means different things on different graphs!
⚠️ Common Mistake
Distance-Time Graph
Horizontal line = Object is STATIONARY
Distance not changing = not moving
Speed-Time Graph
Horizontal line = CONSTANT SPEED
Speed not changing = moving steadily
Click on shapes to see what they mean on a Speed-Time graph:
⚠️ Examiner's Traps & Mark Scheme Tips
❌ TRAP #1: Confusing Distance-Time and Speed-Time
The Mistake: Thinking a flat line always means "stopped"
The Truth: On a speed-time graph, a flat line means constant speed (still moving!)
❌ TRAP #2: Forgetting the "Change in" Keywords
The Mistake: Writing "acceleration = velocity / time"
Mark Scheme Requirement: "acceleration = change in velocity per unit time"
❌ TRAP #3: Area Calculation Errors
The Mistake: Using base × height for a triangle (forgetting the ½)
Correct Formula: Triangle area = ½ × base × height
❌ TRAP #4: Deceleration Sign
The Mistake: Giving deceleration as a positive number
Mark Scheme: Deceleration must be expressed as negative (e.g., -3 m/s²)
❌ TRAP #5: Free Fall Value
The Mistake: Using g = 10 m/s² without checking question requirements
Exam Practice: Use g = 9.8 m/s² unless told "take g = 10 m/s²"
✅ Syllabus Coverage Checklist
Core Content (1.2.4 - 1.2.8)
Supplement Content (1.2.9)
🎯 Quick Revision Summary
📐 Key Formulas
a = Δv / Δt
Δv = v - u
Distance = Area under speed-time graph
g = 9.8 m/s² (≈ 10 m/s²)
🔑 Mark Scheme Keywords
- • "change in velocity per unit time"
- • "gradient of the speed-time graph"
- • "area under the graph"
- • "negative acceleration"
- • "terminal velocity"
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