A cyclist rides along a flat road and then up a steep hill before stopping at the top. Explain how the concepts of scalar and vector quantities apply to the cyclist's distance and displacement during this journey, and explain why the cyclist's weight and mass are different physical quantities.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A cyclist starts from home, travels 500 m along a flat road heading east, then rides 300 m up a steep hill heading north-east before stopping.
Model answer (5 marks)
Distance is a scalar quantity – it has only magnitude. The cyclist covers 500 m on the flat road and 300 m up the hill, so the total distance is 800 m.
Displacement is a vector quantity – it has magnitude and direction. The cyclist’s displacement is the straight‑line distance from the start to the finish point, which lies to the north‑east of the start.
Mass is a scalar quantity that measures the amount of matter in an object and is independent of location. The cyclist’s mass therefore remains the same whether on Earth or elsewhere.
Weight is a force (a vector quantity) produced by the gravitational field acting on the cyclist’s mass. It is measured in newtons and has a direction (downward). Weight would be different on another planet because the gravitational field strength is different, whereas mass would remain unchanged, showing that weight and mass are distinct physical quantities.
Displacement is a vector quantity – it has magnitude and direction. The cyclist’s displacement is the straight‑line distance from the start to the finish point, which lies to the north‑east of the start.
Mass is a scalar quantity that measures the amount of matter in an object and is independent of location. The cyclist’s mass therefore remains the same whether on Earth or elsewhere.
Weight is a force (a vector quantity) produced by the gravitational field acting on the cyclist’s mass. It is measured in newtons and has a direction (downward). Weight would be different on another planet because the gravitational field strength is different, whereas mass would remain unchanged, showing that weight and mass are distinct physical quantities.
Examiner tips
- State that distance is scalar and give the total 800 m; state that displacement is vector and give its magnitude and direction; explain mass as scalar and weight as vector; mention weight changes with gravity but mass does not.
Common mistakes
- Confusing distance with displacement or giving displacement as 800 m; treating mass as a force or weight as a scalar; forgetting to mention the direction of displacement or weight.
Mark scheme (5 marks)
- Distance is a scalar quantity, meaning it has magnitude only (no direction), so the total distance is 800 m
- Displacement is a vector quantity, meaning it has both magnitude and direction, so the cyclist's displacement is the straight-line distance from start to finish point in a stated direction
- Mass is a scalar quantity measuring the amount of matter in an object and does not change with location
- Weight is a force (vector quantity) caused by a gravitational field acting on the cyclist's mass, measured in Newtons
- Weight would differ on another planet (because gravitational field strength differs) whereas mass would remain the same, showing they are different physical quantities
Key terms in this question
scalar · vector · distance · displacement · mass · weight
Related
- All OCR A-Level Physics A (H556) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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