AQA GCSE Physics Foundation (8463), Foundation tier · Forces › Forces and their interactions
Practise Scalar and vector quantities. 6 exam-style questions on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Scalar quantities have size (magnitude) only; vector quantities have size and direction. You need to sort quantities into the two groups and show vectors as arrows. It is usually tested with short recall and tick-box questions, and it underpins the rest of the Forces topic.
Key facts
Scalar = magnitude only
Vector = magnitude and direction
Scalars: distance, speed, mass, time, energy, temperature
Vector arrow: length = magnitude, arrow direction = direction of the quantity
Mass is a scalar (kg); weight is a force, so it is a vector (N)
Notes
Scalars and vectors
A scalar quantity has magnitude (size) only.
A vector quantity has magnitude and an associated direction.
Scalars: distance, speed, mass, time, energy, temperature, power, density.
Vectors: displacement, velocity, acceleration and force (every force, including weight and friction).
Pairs to know
Distance (scalar) and displacement (vector): displacement is the straight-line distance from start to finish, with a direction.
Speed (scalar) and velocity (vector): velocity is speed in a given direction.
Mass (scalar, in kg) and weight (vector, in N): weight is a force, so it has a direction, towards the centre of the Earth.
Drawing vectors as arrows
diagram
A vector quantity can be shown by an arrow.
The length of the arrow shows the magnitude, drawn to a scale.
The direction of the arrow shows the direction of the vector quantity.
Length shows the size (to scale); the arrowhead shows the direction.
Two arrows of the same length pointing opposite ways show vectors of the same size in opposite directions.
How to answer each type of question
Tick-box: identify scalar or vector quantities
1 to 2 marksGrade 3
Ask: does this quantity need a direction to describe it fully?
If yes, it is a vector; if no, it is a scalar.
Tick exactly the number of boxes asked for.
Example. Which two of these are vector quantities? energy / force / mass / speed / velocity
Show the model answerHide the model answer
force (1) velocity (1)
Describe the difference between a scalar and a vector
2 marksGrade 4
Write one sentence about the scalar: magnitude only.
Write one sentence about the vector: magnitude and direction.
Example. Speed is a scalar quantity. Velocity is a vector quantity. Describe the difference between speed and velocity.
Show the model answerHide the model answer
Speed has magnitude (size) only (1). Velocity has magnitude and direction: it is speed in a given direction (1).
Read or draw a vector arrow to scale
1 to 2 marksGrade 5
Use the scale to convert between length and magnitude.
Length = magnitude ÷ value of 1 cm; magnitude = length × value of 1 cm.
Example. A force diagram uses a scale of 1 cm = 10 N. (a) What length of arrow represents a force of 45 N? (b) An arrow on the diagram is 2.5 cm long. What force does it represent?
Show the model answerHide the model answer
(a) 45 ÷ 10 = 4.5 cm (1) (b) 2.5 × 10 = 25 N (1)
Don’t lose marks
Calling mass a vector or weight a scalar. Weight is a force, so it is a vector.
Writing 'a vector has direction' without saying it also has magnitude. You need both for the mark.
Thinking acceleration is a scalar. Acceleration is a change in velocity, so it has a direction.
Thinking energy is a vector because it is 'transferred'. Energy is a scalar.
Drawing force arrows that are not to a consistent scale, so a bigger force has a shorter arrow.
More tips
Memory tricks
Direction test: if it makes sense to add 'to the left' or 'northwards', the quantity is a vector.
Learn the pairs scalar-first: distance/displacement, speed/velocity, mass/weight. The second word in each pair is the vector.
Every force is a vector, so weight, friction, tension and drag are all vectors.
Energy is never a vector: it has no direction, even though it is transferred from place to place.
Exam technique
For 'describe the difference', write one clear sentence about each type of quantity.
In tick-box questions, ticking more boxes than asked for usually scores zero for that part.
Whenever you compare speed with velocity, or distance with displacement, mention direction.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 3
Define scalar and vector quantitiesA scalar has magnitude only; a vector has magnitude and an associated direction.
Grade 4
Sort common quantities into scalars and vectorsDistance, speed, mass, time, energy and temperature are scalars; displacement, velocity, acceleration and force are vectors.
Grade 5
Represent a vector with an arrowThe length of the arrow shows the magnitude and the way it points shows the direction.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
The forecast gives both a size and a direction for the wind. What vector quantity is being described?
Velocity.
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy5 marks
(a) Which of these is a vector quantity? Tick (✓) one box.[1]
Energy
Mass
Temperature
Velocity
(b) Which two of these are scalar quantities? Tick (✓) two boxes.[2]
Acceleration
Displacement
Distance
Force
Time
(c) Describe the difference between a scalar quantity and a vector quantity.[2]
Show the answer and mark scheme
(a)Answer: Velocity
(b)Answer: Distance; Time
(c)Answer: A scalar has magnitude only; a vector has magnitude and direction.
a scalar quantity has magnitude (size) only
a vector quantity has magnitude and (an associated) direction
Question 2Medium4 marks
A weather forecast states: ‘Winds today will reach speeds of up to 50 km/h, blowing from the southwest.’
(a) The forecast gives both a size and a direction for the wind. What vector quantity is being described?[1]
(b) If the forecast had only said ‘winds of up to 50 km/h’, with no direction given, what quantity would this describe?[1]
(c) A hot-air balloon drifts with a steady wind of 50 km/h for 2.0 hours. Explain why knowing only the speed of the wind is not enough to predict where the balloon will be after 2.0 hours.[2]
Show the answer and mark scheme
(a)Answer: Velocity.
(wind) velocity
(b)Answer: Speed.
speed
(c)Answer: Speed only gives the distance travelled (100 km); the wind’s direction (its velocity) is needed to find the balloon’s displacement.
the wind speed only gives the distance the balloon travels (100 km), not the direction it travels in
the direction of the wind (its velocity, a vector) is also needed to find the balloon’s displacement / where it ends up