Scalar and vector quantities — AQA GCSE Physics
Test yourself on Scalar and vector quantities with AQA GCSE practice questions.
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Scalar and vector quantities explained
A scalar quantity is completely described by a number and a unit, its magnitude, with no direction attached.
Read the full explanation
Distance, speed, mass, energy, time and temperature are all scalars. Because there is no direction, scalars of the same kind add as ordinary numbers, so walking 3 km then 4 km always totals 7 km of distance however the route bends. Some kinematic scalars have a vector partner that does carry direction: distance pairs with displacement, and speed with velocity. However, scalars like mass, time, and temperature have no vector counterpart. This distinction is often examined when comparing a winding route between two towns to a straight line.
Vector quantities have magnitude and an associated direction.
A vector quantity needs two things to describe it: a magnitude and an associated direction. Displacement, velocity, acceleration, force, weight and momentum are all vectors, so an answer of '5 N' or '20 m/s' is incomplete unless the direction is given too. The direction matters physically, not just in the writing. A car going round a bend at a steady 30 m/s has constant speed but changing velocity, because its direction keeps changing, so its average velocity between two cameras differs from its average speed. The same reasoning explains why a satellite in a circular orbit is accelerating even though its speed never changes, since the gravitational force keeps altering the direction of its motion.
A vector quantity may be represented by an arrow.
An arrow is the standard way of showing a vector on a diagram because it carries both pieces of information at once. Draw it with a ruler, starting at the object or at the point where the quantity acts, with a single arrowhead showing the direction, and label it with what it represents. A weight arrow is drawn from the object towards the centre of the Earth, which on a diagram of a satellite in orbit is not simply 'down the page'. When several vectors appear on the same diagram, draw them to a consistent scale so that a longer arrow really does mean a larger quantity, and keep every arrow separate rather than joining them into a single line.
The length of the arrow represents the magnitude, and the direction of the arrow the direction of the vector quantity.
When an arrow represents a vector to scale, its length stands for the magnitude and the way it points stands for the direction. Start by choosing and writing down a scale, for example 1 cm represents 10 N. A 35 N force then needs a line 3.5 cm long, measured with a ruler, with the arrowhead placed to show which way the force acts. Reading a diagram reverses the process: measure the arrow, then multiply by the scale, so a 4.2 cm arrow on that scale is 42 N. The scale must stay the same for every arrow on the diagram, otherwise a comparison of lengths says nothing about the comparison of magnitudes.
Your focus
- Classify a list of quantities as scalar or vector and give a reason for each decision.
- Explain why the distance travelled between two towns differs from the displacement.
- Name the vector partner of specific kinematic scalars like distance or speed.
Show all 12 objectives
- Explain why the average speed of a car between two cameras can differ from its average velocity.
- Give a situation in which a velocity changes while the speed stays constant.
- Write a complete vector answer, including both magnitude and direction.
- Draw a labelled arrow to represent a named force acting on an object in a given diagram.
- Decide the correct direction for a weight arrow on a diagram of an object in orbit.
- Identify three faults in a vector diagram whose arrows are unlabelled, double-headed or out of scale.
- Choose and state a suitable scale for drawing a set of vectors in the space provided.
- Draw a vector to scale, with correct length and direction, from a stated magnitude.
- Determine a magnitude by measuring an arrow on a scale diagram and converting using the stated scale.
Scalar and vector quantities exam tips
Marking Points
- one mark for defining a scalar as having magnitude only, with no direction
- one mark for a correct example, such as distance, speed, mass, energy or temperature
- one mark for stating that scalars of the same type add as ordinary numbers
- one mark for correctly pairing a kinematic scalar with its vector partner, such as distance with displacement
- one mark for a vector having a magnitude and an associated direction
- one mark for a correct example, such as displacement, velocity, acceleration, force, weight or momentum
- one mark for stating that velocity changes when direction changes, even if the speed is constant
- one mark for applying this to a curved route, where average speed and average velocity differ
- one mark for the arrow starting at the object or at the point where the quantity acts
- one mark for the arrow pointing in the correct direction, such as towards the centre of the Earth for the weight of an orbiting satellite
- one mark for a single ruled arrow with one arrowhead, labelled with the quantity it represents
- one mark for drawing all the vectors on the diagram to the same scale
- one mark for choosing and stating a scale, such as 1 cm represents 10 N
- one mark for a line drawn and measured to the correct length for the magnitude
- one mark for an arrowhead placed to show the direction of the quantity
- one mark for converting a measured length back to a magnitude using the stated scale
Examiner Tips
- 💡Learn the specific scalar-vector pairs like distance with displacement and speed with velocity, as these are examined most.
- 💡Use the exact phrase 'magnitude only', which is the wording the mark scheme accepts.
- 💡Finish every vector answer with a direction, such as 'to the right' or 'towards the centre of the Earth'.
- 💡When a question says a road is not straight, the examiner is signalling a direction change, so mention it.
- 💡Quote both halves of the definition, magnitude and direction, since a half definition is often only half the mark.
- 💡Check which object the force acts on before you decide where the arrow starts.
- 💡Use a ruler even for a rough diagram; a wavy line can be read as the wrong length.
- 💡Label the arrow with the name of the quantity, not just a number.
- 💡Write the scale on the diagram itself; a scale kept only in your head cannot be credited.
- 💡Choose a scale that makes the longest arrow fill most of the space available, which reduces measuring error.
- 💡Measure to the nearest millimetre and state the answer to a sensible number of figures.
Common Mistakes
- calling weight a scalar, when it is a force and therefore a vector
- claiming every scalar has a vector partner, forgetting that mass, time, and temperature do not
- listing velocity, force or acceleration among the scalars
- defining a vector only as 'something drawn with an arrow'
- calling speed a vector because the vehicle is obviously going somewhere
- giving a numerical answer for a vector and leaving out the direction
- assuming a vector must have a large magnitude
- saying a satellite in circular orbit is not accelerating because its speed is constant
- drawing a double-headed arrow, so no direction is shown
- drawing the gravitational force on an orbiting object straight down the page instead of towards the centre of the Earth
- sketching arrows freehand at arbitrary lengths when a scale is in use
- leaving arrows unlabelled so the examiner cannot tell which force is which
- drawing the arrow from the Earth to the satellite when the force asked for acts on the satellite
- drawing arrows at any convenient length and writing the value beside them instead
- changing the scale part-way through a diagram, so arrows can no longer be compared
- measuring the arrow correctly but forgetting to multiply by the scale
- giving an answer in centimetres rather than converting to newtons or metres per second
- giving a magnitude with no direction when the question asks for a vector