1.2 Motion Basics
Speed, Velocity & Distance-Time Graphs
The Hook: Why Fast Isn't Always Fast
Imagine two racers. One runs in a perfectly straight line at 10 m/s. The other zigzags at 10 m/s but ends up back where they started. Both moved at the same speed, but who actually got somewhere? This is the difference between speed (how fast) and velocity (how fast in a direction).
Real World: GPS navigation doesn't just track your speedometer—it tracks your velocity. That's how it knows you took a wrong turn and need to reroute!
Interactive: Speed vs Velocity Racer
Watch what happens when we race a car on two different paths at the same speed:
STRAIGHT PATH (Constant Velocity)
Distance covered: 50m
WINDING PATH (Same Speed, Different Direction)
Distance covered: 50m (but displacement is less!)
📊 Analysis at 5s:
Both cars have the same speed (10 m/s reading on speedometer)
But different velocities (blue car moving east, orange car changing direction)
Core Definitions (Mark Scheme Keywords)
1.2.1 Speed (Scalar Quantity)
Definition: Speed is the distance travelled per unit time.
v = s / t
where v = speed (m/s), s = distance (m), t = time (s)
⚠️ Unit Police: Speed MUST be in m/s (meters per second) or km/h—never mix units!
1.2.2 Velocity (Vector Quantity)
Definition: Velocity is speed in a given direction.
Example: "20 m/s North" or "50 km/h towards the school"
If direction changes, velocity changes—even if speed stays the same!
1.2.3 Average Speed
Definition: Average speed = total distance travelled / total time taken
average speed = (total distance) / (total time)
Interactive: Distance-Time Graph
A distance-time graph shows how far an object has travelled over time. The gradient (slope) tells us the speed.
Visual Scene
Distance-Time Graph
🔍 What the Graph Shows:
- • Steeper line = Faster speed (more distance in same time)
- • Horizontal line = Stopped (no distance covered, time passing)
- • Gradient = Speed (rise ÷ run = distance ÷ time)
At 0s: Speed = 0.0 m/s
Interactive: Average Speed Calculator
A common exam trap! Let's see why you can't just average the speeds.
✅ CORRECT Method (Syllabus 1.2.3)
Average Speed = Total Distance ÷ Total Time
= (100 + 100) ÷ (10 + 20)
= 6.67 m/s
❌ WRONG Method (Common Trap!)
Just averaging the two speeds:
= [(100÷10) + (100÷20)] ÷ 2
= 7.50 m/s
Examiner's Traps (Don't Lose Marks!)
Trap 1: Speed vs Velocity
❌ "The car moved at 20 m/s velocity" (no direction given)
✅ "The car moved at 20 m/s speed" OR "20 m/s North"
Trap 2: Unit Mixing
❌ Distance in km, time in seconds → Must convert first!
✅ Always use SI units: meters (m) and seconds (s)
Trap 3: Distance-Time Graph Gradient
❌ "The gradient is 5" (no units or meaning)
✅ "The gradient is 5 m/s, which represents the speed"
Syllabus Checklist (1.2.1-1.2.3 Core)
Define speed as distance travelled per unit time
Recall and use v = s/t
Define velocity as speed in a given direction
Recall and use average speed = total distance / total time
Sketch and interpret distance-time graphs
Calculate speed from gradient of distance-time graph
🎓 Ready for More?
You've mastered the Core content for Motion Basics! Next up:
- • 1.2.4-1.2.7: Speed-Time Graphs & Acceleration
- • 1.2.9-1.2.13 (Supplement): Advanced acceleration calculations
- • Practice Questions: Paper 2, 4, and 6 exam-style problems
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