Scalar and Vector Quantities
Learn Scalar and Vector Quantities for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Scalar quantities have size only, while vector quantities such as force and velocity have both size and direction.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
A scalar quantity has magnitude only. A vector quantity has both magnitude and direction.
Scalars include distance, speed, mass, energy, time and temperature. Vectors include displacement, velocity, force, weight, acceleration and momentum. The distinction matters because vectors can cancel each other out while scalars cannot.
Distance and displacement illustrate this. Walking 5 m east then 5 m west covers a distance of 10 m, because distance simply accumulates. But the displacement is zero, because the two movements are in opposite directions and cancel. The same logic applies to speed and velocity.
Revision notes
The definitions
A scalar quantity has magnitude, or size, only.
A vector quantity has both magnitude and direction. Vectors are often represented by an arrow: the length shows the magnitude and the direction of the arrow shows the direction.
Which is which
Scalars: distance, speed, mass, energy, time, temperature.
Vectors: displacement, velocity, force, weight, acceleration, momentum. Note the pairs — distance and displacement, speed and velocity — where one is scalar and the other vector.
Why it matters
Vectors in opposite directions can cancel; scalars cannot.
Walking 5 m east then 5 m west gives a distance of 10 m but a displacement of zero. A car travelling in a circle at constant speed has a changing velocity, because its direction changes.
Key points
- A scalar has magnitude only.
- A vector has magnitude and direction.
- Distance and speed are scalars.
- Displacement and velocity are vectors.
- Force and weight are vectors.
- Vectors in opposite directions can cancel.
Worked examples
Example 1
State the difference between a scalar and a vector quantity. [2 marks]
Model answer
A scalar quantity has magnitude only (1 mark). A vector quantity has both magnitude and direction (1 mark).
Example 2
A person walks 5 m east then 5 m west. State the distance travelled and the displacement. [2 marks]
Model answer
The distance travelled is 10 m (1 mark). The displacement is zero, because the two movements are in opposite directions and cancel (1 mark).
Example 3
Explain why a car moving in a circle at a constant speed has a changing velocity. [2 marks]
Model answer
Velocity is a vector, so it has both magnitude and direction (1 mark). Although the speed stays constant, the direction is continually changing, so the velocity changes (1 mark).
Common mistakes
Calling weight a scalar.
Weight is a force, so it is a vector with direction.
Treating displacement as the same as distance.
Displacement includes direction and can be zero when distance is not.
Saying constant speed means constant velocity.
If the direction changes, the velocity changes even at constant speed.
Calling mass a vector.
Mass is a scalar; weight is the vector force.
Exam tips
- Learn the scalar and vector lists as two separate sets.
- Note the paired quantities — distance/displacement, speed/velocity.
- Use the word direction when defining a vector.
- Remember vectors can cancel; scalars accumulate.
Key terms
- Scalar
- A quantity with magnitude only.
- Vector
- A quantity with magnitude and direction.
- Displacement
- The straight-line distance and direction from start to finish.
- Magnitude
- The size of a quantity.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.