Distance and displacement — AQA GCSE Physics
Test yourself on Distance and displacement with AQA GCSE practice questions.
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Distance and displacement explained
Distance is the total length of the path travelled, measured along whatever route was actually taken.
Read the full explanation
It is a scalar, which means it is fully described by a magnitude and a unit, such as 350 m or 12 km, with no direction attached. A car's odometer measures distance: drive one lap of a circuit and it records the whole lap even though you finish where you started. Distances add as ordinary numbers, so walking three metres east and then four metres west gives a distance of seven metres. Because it carries no direction, a distance can never be negative and never decreases as a journey continues. Speed, mass, time, energy and temperature are scalars too; force, velocity, displacement, acceleration and momentum are not.
Displacement includes both the distance an object moves, measured in a straight line from the start point to the finish point and the direction of that straight line.
Displacement is measured in a straight line from where the object started to where it finished, and it carries a direction as well as a length. On a scale map of a winding railway, the distance travelled is the length of the track while the displacement is the straight arrow drawn from the first station to the second, measured with a ruler and converted using the scale. Walk three metres east and then four metres north and the distance is seven metres, but the displacement is five metres on a bearing of 037 degrees, because the two legs combine as a right-angled triangle. Any journey that returns to its starting point has zero displacement however far it travelled, and displacement can never exceed distance.
Displacement is a vector quantity.
Calling displacement a vector means it needs both a size and a direction before it is fully described, and that it combines by geometry rather than by simple addition. On a diagram a vector is drawn as an arrow whose length is drawn to scale and whose direction is the direction of the quantity. Along a single line, direction can be handled with signs: taking east as positive, a displacement of five metres west is written as negative five metres, and adding eight metres east to that gives three metres east. In two dimensions the arrows are joined tip to tail and the resultant runs from the start of the first to the end of the last. The other vectors on this course are force, velocity, acceleration, momentum and weight.
Students should be able to express a displacement in terms of both the magnitude and direction.
Expressing a displacement properly means writing three things: a number, a unit and a direction. Saying 8.5 km is incomplete; 8.5 km due north, or 8.5 km on a bearing of 040 degrees, is a displacement. Acceptable ways of giving the direction include a compass point, a three-figure bearing measured clockwise from north, an angle to a stated line, or simply to the right or upwards where the situation makes that unambiguous. Along a straight line a sign will do, provided the positive direction has been stated. When the displacement is taken from a scale diagram, measure the straight line from start to finish with a ruler, convert it with the scale, then measure the angle with a protractor. A magnitude on its own always loses the direction mark.
Your focus
- Classify given quantities as scalar or vector and justify each choice.
- Calculate the total distance travelled on a route made up of several legs.
- Explain why the distance around a closed loop is not zero.
Show all 12 objectives
- Determine a displacement from a scale drawing, giving both magnitude and direction.
- Compare the distance and the displacement for a journey that changes direction.
- Explain why a closed-loop journey has zero displacement.
- Represent a displacement as a scaled arrow with a stated direction.
- Add two displacements along a line using a sign convention.
- Explain the difference in the way scalars and vectors are combined.
- Judge whether a quoted answer is a complete displacement and supply the missing direction where one is needed.
- Measure a displacement from a scale diagram using a ruler and a protractor.
- Convert a direction expressed as a compass point into a three-figure bearing.
Distance and displacement exam tips
Marking Points
- one mark for distance described as how far an object moves, measured along its path
- one mark for a scalar having magnitude only, with no direction
- one mark for adding distances as ordinary numbers regardless of direction
- one mark for a correct further example of a scalar quantity
- one mark for the straight line measured from the start point to the finish point
- one mark for a direction stated as well as a magnitude
- one mark for measuring a displacement from a scale drawing and applying the scale
- one mark for recognising that the displacement is zero for a journey that returns to its start
- one mark for a vector having both magnitude and direction
- one mark for representing a vector as an arrow drawn to scale in the correct direction
- one mark for using positive and negative signs for opposite directions along a line
- one mark for combining displacements tip to tail to find a resultant
- one mark for the magnitude of the displacement with its unit
- one mark for a direction given as a bearing, a compass point or an angle to a stated line
- one mark for measuring the straight line from start to finish rather than along the path
- one mark for applying the scale of the drawing correctly
Examiner Tips
- 💡Scalar means one number and a unit; if a direction appears, the quantity is a vector.
- 💡For any curved route, the distance is always greater than the displacement.
- 💡Measure with a ruler and show the scale conversion; both steps are credited.
- 💡If the start and the finish coincide, write zero straight away without calculating.
- 💡State your positive direction before using signs; examiners accept either choice if it is declared.
- 💡Draw the arrow, because a labelled diagram often carries the mark on its own.
- 💡Write the direction in the same breath as the number; a displacement without it is half an answer.
- 💡Use the scale printed on the figure rather than assuming one.
Common Mistakes
- giving a direction with a distance, which turns it into a displacement
- using the straight-line separation of start and finish as the distance travelled
- calling force or velocity a scalar
- allowing a distance to decrease part way through a journey
- quoting a displacement with no direction attached
- adding the legs of a journey arithmetically instead of combining them as a triangle
- using the path length as the displacement on a curved route
- forgetting to apply the scale when measuring from a drawing
- stating the magnitude and treating the answer as complete
- adding vectors that point in different directions arithmetically
- drawing an arrow with no scale and no stated direction
- treating a negative displacement as a negative distance
- giving the magnitude only and stopping there
- describing the direction as forwards when no reference direction has been stated
- measuring the route rather than the straight line when using a scale drawing
- quoting a bearing measured anticlockwise or from the wrong reference direction