Distance and displacement — AQA GCSE Combined Science
Test yourself on Distance and displacement with AQA GCSE practice questions.
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Distance and displacement explained
Distance measures how far an object travels along its actual path, regardless of which way it went.
Read the full explanation
Because no direction is needed, distance is a scalar quantity and is fully described by a magnitude with a unit, such as 5 m or 3 km. If you walk 3 m east then 4 m west, the distance travelled is 7 m even though you finish only 1 m from the start. Displacement is different: it is the straight-line distance from start to finish together with the direction, so it is a vector. In the same walk the displacement is 1 m west. Distance is always positive and never decreases as the object moves, while displacement can be zero if you return to the starting point.
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 a vector quantity.
Displacement is the straight-line separation of an object's finish point from its start point, together with the direction of that line. It is not the total path length travelled. For example, a runner who completes one 400 m lap on a track finishes at the start point, so the displacement is 0 m even though the distance travelled is 400 m. If a walker moves 3 m east then 4 m north, the distance travelled is 7 m, but the displacement is 5 m in a direction between east and north, found by drawing the two legs tip-to-tail and measuring the closing straight line. Because displacement has both magnitude and direction, it is a vector quantity; distance has magnitude only and is a scalar. Displacement can be positive or negative along a chosen line, and zero when start and finish coincide.
Students should be able to express a displacement in terms of both the magnitude and direction.
Expressing a displacement means giving two pieces of information: how far the finish point is from the start point in a straight line, and the direction of that line. The magnitude is a length, such as 5 m, and the direction may be given as a compass direction, a bearing, or an angle from a stated line. For example, a displacement of 5 m on a bearing of 053° tells you both the straight-line distance and the direction. To produce this, draw the journey as a vector diagram, join start to finish with a straight line, measure its length using the scale, and measure its angle from a reference direction such as north. A displacement written without direction is incomplete because it does not tell you where the finish point lies.
Your focus
- State that distance is the total path length travelled and is a scalar quantity.
- Compare distance with displacement using a simple journey example.
- Quote distance values with correct units and no direction.
Show all 9 objectives
- State that displacement is the straight-line distance from start point to finish point together with its direction.
- Identify displacement as a vector quantity and distance as a scalar quantity.
- Calculate or measure the magnitude and direction of a displacement for a simple two-part journey.
- Write a displacement as a magnitude with a unit together with a direction.
- Measure the magnitude and direction of a displacement from a scale diagram.
- Convert a measured angle into a three-figure bearing when required.
Distance and displacement exam tips
Marking Points
- Define distance as the total length of the path travelled by an object, measured along the route taken.
- State that distance has magnitude only and no direction, so it is a scalar quantity.
- Give the unit of distance as metres or a suitable multiple such as kilometres, and include the unit when quoting a value.
- Distinguish distance from displacement, which is the straight-line distance from start to finish in a stated direction and is a vector.
- Use a worked example, such as 3 m east then 4 m west giving a distance of 7 m but a displacement of 1 m west.
- Explain that distance is always positive and does not decrease, whereas displacement can be zero when the object returns to its start.
- Defines displacement as the straight-line distance from start point to finish point, not the total path length.
- States that displacement includes the direction of the straight line from start to finish.
- Classifies displacement as a vector quantity because it has both magnitude and direction.
- Distinguishes displacement from distance, which is a scalar and measures the whole path travelled.
- Applies the idea to a closed path, such as one full lap, where displacement is zero but distance is not.
- Uses a scale drawing or vector triangle to find the magnitude and direction of a resultant displacement.
- States a numerical magnitude with a unit for the straight-line distance from start to finish.
- States a direction using a compass point, a bearing, or an angle from a named reference line.
- Uses a scale diagram to measure the straight-line length and the angle of the displacement.
- Converts a measured angle into a three-figure bearing when the question requires a bearing.
- Checks that the magnitude and direction refer to the same straight line from start point to finish point.
- Recognises that changing either the magnitude or the direction changes the displacement.
Examiner Tips
- 💡When asked to classify a quantity, state both that distance is scalar and that it has magnitude but no direction.
- 💡Use a short path example to show the difference between distance and displacement clearly.
- 💡Always attach the correct unit to a distance value, for example 12 m rather than just 12.
- 💡Underline the words 'straight line' and 'direction' in the question so both parts of the displacement definition are addressed.
- 💡When a journey has two legs, sketch them tip-to-tail and draw the closing straight line before calculating anything.
- 💡Check whether the question asks for distance or displacement; a full lap or a return journey often has zero displacement.
- 💡Choose a sensible scale for a vector diagram and write it down so the marker can follow your measurement.
- 💡Give bearings as three-figure angles, for example 053° rather than 53°.
- 💡Include the unit with the magnitude and name the reference direction used for the angle.
Common Mistakes
- Confusing distance with displacement; correction: distance follows the whole path, while displacement is the straight line from start to finish with a direction.
- Giving a direction with a distance value; correction: distance is a scalar, so only a magnitude and unit are needed.
- Thinking distance must be measured in a straight line; correction: distance is measured along the actual path taken, however curved it is.
- Treating displacement as the total distance travelled: correct this by identifying the straight line from start to finish and ignoring the route taken.
- Giving only a number for displacement: correct this by always adding a direction, such as '5 m north-east' or '5 m on a bearing of 053°'.
- Assuming displacement must be positive: correct this by allowing negative values when the finish point lies in the opposite direction along a chosen axis.
- Writing only a magnitude, such as '5 m': correct this by adding the direction, for example '5 m north'.
- Writing only a direction, such as 'north': correct this by adding the straight-line distance with its unit.
- Measuring the angle from the wrong reference line: correct this by marking north or the stated reference clearly before measuring.