What you'll learn
This revision guide covers the fundamental concepts of motion that form the foundation of GCSE Physics kinematics. You'll learn to distinguish between scalar and vector quantities, understand how distance differs from displacement, and calculate both speed and velocity using appropriate equations. These concepts appear regularly in AQA GCSE Physics exams and are essential for more advanced motion topics.
Key terms and definitions
Scalar quantity — A physical quantity that has magnitude (size) only, such as distance, speed, mass, or time.
Vector quantity — A physical quantity that has both magnitude and direction, such as displacement, velocity, force, or acceleration.
Distance — The total length of the path travelled by an object, measured in metres (m). Distance is a scalar quantity.
Displacement — The straight-line distance from an object's starting position to its finishing position, including the direction. Displacement is a vector quantity measured in metres (m).
Speed — The rate of change of distance; how fast an object is moving regardless of direction. Speed is a scalar quantity measured in metres per second (m/s).
Velocity — The rate of change of displacement; the speed of an object in a specified direction. Velocity is a vector quantity measured in metres per second (m/s).
Average speed — The total distance travelled divided by the total time taken for a journey.
Uniform motion — Movement at constant speed in a straight line, where both speed and velocity remain unchanged.
Core concepts
Scalar versus vector quantities
Understanding the difference between scalars and vectors is crucial for this topic.
Scalar quantities have magnitude only:
- Distance: "The car travelled 500 m"
- Speed: "The cyclist moved at 8 m/s"
- Time: "The journey took 45 s"
- Mass: "The object has a mass of 12 kg"
Vector quantities have both magnitude and direction:
- Displacement: "The ship moved 300 m north"
- Velocity: "The aircraft flew at 250 m/s eastward"
- Force: "A 50 N push to the right"
- Acceleration: "The car accelerated at 3 m/s² forward"
In AQA GCSE exams, you must be able to identify whether a quantity is scalar or vector and explain why. Remember: if direction matters, it's a vector.
Distance and displacement
These terms are often confused but represent different concepts.
Distance is the total path length travelled. If you walk 4 m forward, then 3 m backward, you have travelled a total distance of 7 m. Distance is always positive and never decreases during a journey.
Displacement is measured from start to finish in a straight line, with direction specified. Using the same example (4 m forward, then 3 m backward), your displacement is 1 m forward from your starting point. Displacement can be positive, negative, or zero.
Consider a runner completing one lap of a 400 m athletics track:
- Distance travelled = 400 m
- Displacement = 0 m (they finish where they started)
The displacement is zero because the starting and finishing positions are the same, even though the runner covered significant distance.
When describing displacement, you must include direction. This can be specified as:
- Cardinal directions: north, south, east, west
- Bearing: "050° from north"
- Relative terms: left, right, forward, backward
- Positive/negative values: +10 m or -10 m along a defined axis
Speed and velocity
The relationship between speed and velocity mirrors that of distance and displacement.
Speed tells you how fast something is moving:
- It is calculated from distance travelled
- It has no directional component
- It is always positive
- Example: "The train travels at 45 m/s"
Velocity tells you how fast something is moving in a specific direction:
- It is calculated from displacement
- It must include direction
- It can be positive or negative depending on the chosen reference frame
- Example: "The boat moves at 12 m/s due south"
The key equation for speed is:
speed = distance ÷ time
Or using symbols: v = s ÷ t
Where:
- v = speed in metres per second (m/s)
- s = distance in metres (m)
- t = time in seconds (s)
This equation can be rearranged:
- distance = speed × time (s = v × t)
- time = distance ÷ speed (t = s ÷ v)
For velocity, the equivalent equation is:
velocity = displacement ÷ time
The symbols and units are identical, but displacement (with direction) replaces distance.
Average speed calculations
Most journeys involve varying speeds. Average speed is calculated using total distance and total time:
average speed = total distance travelled ÷ total time taken
Important points about average speed:
- Use the complete journey distance and time
- Don't average the individual speeds unless time intervals are equal
- Stationary periods count as part of total time
- Average speed is typically lower than maximum speed during a journey
For example, a bus journey from Kingston to Montego Bay (180 km) taking 3 hours has an average speed of 60 km/h, even though the bus may have travelled at 80 km/h on highways and stopped completely at traffic lights.
Units and conversions
Speed and velocity appear in different units depending on context:
- metres per second (m/s) — standard SI unit used in calculations
- kilometres per hour (km/h) — common for vehicles
- miles per hour (mph) — used in some Caribbean and UK contexts
You may need to convert between units in exam questions.
To convert km/h to m/s: divide by 3.6
- Example: 36 km/h = 36 ÷ 3.6 = 10 m/s
To convert m/s to km/h: multiply by 3.6
- Example: 25 m/s = 25 × 3.6 = 90 km/h
The conversion works because:
- 1 km = 1000 m
- 1 hour = 3600 s
- Therefore 1 km/h = 1000 m ÷ 3600 s = 1/3.6 m/s
Typical speeds
You should be familiar with typical walking, running, and cycling speeds:
- Walking: approximately 1.5 m/s
- Running: approximately 3 m/s
- Cycling: approximately 6 m/s
- Sound in air: approximately 330 m/s
- Car on motorway: approximately 30 m/s (108 km/h or 70 mph)
These values help you check whether calculated answers are realistic.
Worked examples
Example 1: Distance versus displacement
Question: A student walks 80 m east from the school gate to the science block, then 60 m north to the library.
(a) Calculate the total distance walked. [1 mark]
(b) Calculate the magnitude of the student's displacement from the school gate. [2 marks]
Solution:
(a) Total distance = 80 m + 60 m = 140 m ✓
(b) The displacement forms the hypotenuse of a right-angled triangle.
Using Pythagoras' theorem: displacement² = 80² + 60² displacement² = 6400 + 3600 = 10000 displacement = √10000 = 100 m ✓✓
(Award 1 mark for correct method, 1 mark for correct answer)
The full displacement would be "100 m at a bearing of approximately 037°" or "100 m north-east", though the question only asks for magnitude.
Example 2: Average speed calculation
Question: A taxi travels 15 km from Bridgetown to the airport in 20 minutes.
(a) Calculate the average speed of the taxi in km/h. [2 marks]
(b) Convert this speed to m/s. [2 marks]
Solution:
(a) First convert time to hours: 20 minutes = 20/60 hours = 1/3 hours ✓
average speed = distance ÷ time average speed = 15 ÷ (1/3) = 15 × 3 = 45 km/h ✓
(b) To convert km/h to m/s, divide by 3.6: 45 ÷ 3.6 ✓ = 12.5 m/s ✓
Example 3: Speed with direction (velocity)
Question: A ferry travels 9.0 km due north in 15 minutes, then 12 km due east in 20 minutes.
(a) State the ferry's average speed in m/s for the whole journey. [3 marks]
(b) Explain why the ferry's average velocity is different from its average speed. [2 marks]
Solution:
(a) Total distance = 9.0 + 12 = 21 km = 21000 m ✓ Total time = 15 + 20 = 35 minutes = 35 × 60 = 2100 s ✓
average speed = 21000 ÷ 2100 = 10 m/s ✓
(b) Average velocity is different because it is calculated using displacement (straight-line distance from start to finish) ✓ rather than the total distance travelled along the path. The displacement is less than the total distance. ✓
Common mistakes and how to avoid them
Confusing distance with displacement: Remember that distance is the path length (always positive) while displacement is the straight-line change in position with direction. If an object returns to its starting point, displacement is zero but distance is not.
Forgetting to include direction for vectors: When answering questions about displacement or velocity, always state the direction. "30 m" is incomplete for displacement; you need "30 m north" or similar.
Incorrectly calculating average speed: Don't add speeds and divide by 2 unless the time spent at each speed is equal. Always use total distance ÷ total time for the complete journey.
Unit errors: Ensure all quantities are in compatible units before calculating. Convert km to m and hours/minutes to seconds when using the standard equations. A common error is using time in minutes with distance in metres, giving incorrect units for speed.
Misunderstanding zero values: An object can have zero displacement but non-zero distance (completing a lap), or zero velocity but have travelled a distance (moving then returning). Think carefully about what these values mean.
Rounding too early: Keep full calculator values during multi-step calculations and only round the final answer to an appropriate number of significant figures (usually 2 or 3 for GCSE).
Exam technique for "Distance, displacement, speed and velocity"
Command words matter: "State" requires a simple answer without explanation. "Calculate" requires you to show working clearly with correct units. "Explain" requires you to give reasons using physics principles. "Describe the difference" requires you to give distinct points about each term.
Show your working: Even if you get the final answer wrong, you can gain method marks. Write the equation, substitute values, then calculate. For a 3-mark calculation, typically 1 mark is for the correct equation, 1 for correct substitution, 1 for the answer with units.
Check units in your answer: Speed or velocity without units (m/s, km/h, etc.) will lose the final mark. Distance without metres or displacement without direction will also lose marks.
Use given values carefully: If a question provides values to a certain number of significant figures, match this in your answer. If distance is given as 250 m (2 sig figs), give your answer to 2 significant figures.
Quick revision summary
Distance is a scalar measuring path length; displacement is a vector measuring straight-line position change with direction. Speed is a scalar calculated from distance ÷ time; velocity is a vector calculated from displacement ÷ time. Scalars have magnitude only; vectors have magnitude and direction. Average speed uses total distance and total time. Always include correct units (m, m/s) and direction for vectors. Remember typical speeds: walking ≈ 1.5 m/s, running ≈ 3 m/s, cycling ≈ 6 m/s.