Distance = displacement (they are numerically equal).
For motion that changes direction: distance > |displacement|.
Speed
SPEED is the rate of change of distance — scalar quantity.
EQUATION:
v = d ÷ t (for uniform/average speed)
v = speed (m/s)
d = distance (m)
t = time (s)
Typical speeds:
Walking: ~1.5 m/s
Running: ~3 m/s
Cycling: ~6 m/s
Car on motorway: ~30 m/s
Speed of sound in air: ~340 m/s
Speed of light in vacuum: 3 × 10⁸ m/s
SPEED IS NOT CONSTANT in most real motion — the equation gives AVERAGE speed.
UNIT CONVERSIONS:
1 m/s = 3.6 km/h
30 m/s ≈ 108 km/h
Velocity
VELOCITY is the rate of change of displacement — vector quantity.
velocity = displacement ÷ time
Velocity has the SAME MAGNITUDE as speed when moving in a straight line.
Velocity DIFFERS from speed when direction changes.
EXAMPLE:
A car drives 100 m north in 10 s → velocity = 10 m/s north, speed = 10 m/s.
A car drives 100 m north then 100 m south in 20 s total:
Speed = 200/20 = 10 m/s
Velocity = 0/20 = 0 m/s (back at start → displacement = 0)
CHANGING VELOCITY:
Velocity changes when speed changes OR when direction changes.
A car going around a bend at constant speed has CHANGING VELOCITY (direction changes).
Changing velocity = acceleration.
⚠️ Common Mistake
Speed is scalar (magnitude only). Velocity is vector (magnitude AND direction). A car travelling in a circle at constant SPEED has changing VELOCITY — direction is always changing. Average speed = total distance ÷ total time (not displacement).
📐 Variables
vSpeed or velocity (v) is measured in m/s (m/s)
dDistance (d) is measured in metres (m)
sDisplacement (s) is measured in metres (m)
tTime (t) is measured in seconds (s)
📐 Key Equations
v = d ÷ t (average speed)
📌 Key Note
Distance: scalar, total path. Displacement: vector, start to finish with direction. Speed = d/t (scalar). Velocity = displacement/t (vector). Speed = |velocity| for straight-line motion. Constant speed in a circle = changing velocity. Average speed: total distance ÷ total time.
🎯 Matching Activity — Distance, Speed, Velocity
Match each calculation or concept to the correct value or description. — drag the symbols on the right to match the component names on the left.
Speed = 5 m/s
Drop here
Velocity = 0 m/s
Drop here
Distance = 7 m
Drop here
Changing velocity
Drop here
Travels 100 m in 20 s — v = 100 ÷ 20 = 5 m/s
Walks 3 m north and 4 m east — total path length = 3 + 4
Car driving in a circle at constant speed — direction (and therefore velocity) changes
Walks 400 m around a circular track and returns to start in 200 s
⚽ FIFA Worked Examples
Speed Calculation
A car travels 450 m in 30 s. Calculate its average speed.
F
v = d ÷ t
I
d = 450 m, t = 30 s
F
v = 450 ÷ 30
A
v = 15 m/s
🎯 Test Yourself
Question 1 of 2
1. A cyclist rides 600 m east in 60 s, then 600 m west in 60 s. What is the average speed and average velocity for the whole journey?
2. A car drives around a roundabout at constant speed of 10 m/s. Is its velocity constant?
⭐ How Well Do You Understand This Topic?
Be honest with yourself — this helps you know what to revise!
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