Distinguish scalar and vector quantities
Use magnitude alone for scalars and magnitude with direction for vectors.
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Distinguish a numerical size from a direction.
- Recognise common physical quantities and units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What extra information accompanies a vector's magnitude?
What you will learn
- Classify the specified scalar and vector quantities.
- Explain why a direction change can change velocity at constant speed.
Ask whether direction is part of the quantity
A scalar has magnitude only. Distance, speed, time, mass, energy and temperature are the syllabus scalar examples. A direction is not needed to specify a time of 12 s or an energy of 40 J. A negative temperature value does not turn temperature into a vector; a sign is not automatically a spatial direction.
A vector has magnitude and direction. The syllabus examples are force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength. Weight is the gravitational force, so its direction matters, even though mass is scalar. Some of these quantities are developed in later sections; their classification can be learned now.
Keep speed and velocity separate
Speed 5 m/s describes how quickly a body moves. Velocity 5 m/s east adds the direction of motion. Turning from east to north changes velocity even if speed stays 5 m/s. A vector arrow indicates direction; under a stated scale its length represents magnitude.
A journey's distance counts the whole path, while its displacement is the overall directed position change. Returning to the start can give non-zero distance with zero displacement. Do not infer that all motion ceased merely because the net displacement is zero. Later resultant calculations add vector components, rather than adding every magnitude as if all directions matched.
Sources for this lesson
Pause and explain
Which pair contains a scalar followed by a vector?
Worked example
A car turns north while maintaining speed 8 m/s. Has its velocity changed?
Show the worked solution
- Its speed magnitude remains 8 m/s.
- The direction of motion changes.
- Velocity includes direction, so velocity changes.
Answer Yes; direction changes even though speed stays constant.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Classify distance, speed, time, mass, energy and temperature.
Give me a hint
Ask whether a spatial direction is needed to specify each quantity.
Compare my reasoning
- Distance and speed use magnitudes without direction.
- Time and mass likewise require no direction.
- Energy and temperature are scalars too.
All six are scalars.
Look for these in your work
- Include all specified examples.
- Use the magnitude-only definition.
Classify force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength.
Give me a hint
Each quantity has a physically relevant direction.
Compare my reasoning
- Force and weight act in specified directions.
- Velocity, acceleration and momentum are directed motion quantities.
- Electric and gravitational field strengths have directions as well.
All seven are vectors.
Look for these in your work
- Include both field quantities.
- Distinguish weight from mass.
A runner completes a loop at constant speed and returns to the start. Explain whether velocity was constant and whether distance was zero.
Give me a hint
Separate the path, the net position change and direction during motion.
Compare my reasoning
- Direction changes around the loop, so velocity is not constant.
- Distance is the non-zero loop length.
- Net displacement is zero because the runner returns to the start.
Velocity changes; distance is non-zero; net displacement is zero.
Look for these in your work
- Use direction to discuss velocity.
- Separate distance from displacement.
Common mistakes
- Mass is scalar; weight is a vector force.
- A negative scalar reading does not create a spatial direction.
- Equal speed does not guarantee equal velocity.
What can you explain now?
Is gravitational field strength scalar or vector?
Compare with the explanation
Vector.
Its direction specifies the force per unit mass on an object.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
List all six specified scalars and seven specified vectors, then explain a direction change at constant speed.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.