A cyclist travels 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 motion during this journey, and describe what the velocity-time graph of this journey would show about the cyclist's acceleration.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A cyclist starts from rest, accelerates along a flat road, then decelerates as they climb a steep hill, eventually coming to a stop at the top of the hill.
Model answer (5 marks)
Distance is a scalar quantity – it has only magnitude and no direction.
Displacement is a vector quantity – it has magnitude and a direction, being the straight‑line distance from start to finish.
Velocity is a vector quantity – it gives the speed together with the direction of motion; speed alone is scalar.
On a velocity‑time graph the flat‑road section shows a positive gradient, indicating the cyclist’s velocity is increasing (accelerating).
During the hill the gradient becomes negative, showing the cyclist is decelerating until the velocity reaches zero at the top.
Displacement is a vector quantity – it has magnitude and a direction, being the straight‑line distance from start to finish.
Velocity is a vector quantity – it gives the speed together with the direction of motion; speed alone is scalar.
On a velocity‑time graph the flat‑road section shows a positive gradient, indicating the cyclist’s velocity is increasing (accelerating).
During the hill the gradient becomes negative, showing the cyclist is decelerating until the velocity reaches zero at the top.
Examiner tips
- Use the exact terms ‘scalar’ and ‘vector’ and give the definition for each quantity. Show the sign of the gradient on the v‑t graph to link it to acceleration. Keep the answer concise – one sentence per point. Mention that speed is scalar but velocity is vector to demonstrate understanding.
Common mistakes
- Confusing speed with velocity or omitting the direction component. Describing distance as a vector or forgetting that displacement is a straight‑line vector. Mislabeling the gradient on the v‑t graph (e.g., saying a positive gradient means deceleration).
Mark scheme (5 marks)
- Distance is a scalar quantity — it has magnitude only / does not depend on direction
- Displacement is a vector quantity — it has both magnitude and direction / is the straight line between starting and finishing points
- Velocity is a vector quantity — it gives speed in a given direction / speed is scalar but velocity is vector
- On the velocity-time graph, a positive gradient during the flat section shows the cyclist is accelerating (velocity is increasing)
- A negative gradient on the velocity-time graph during the hill section shows the cyclist is decelerating / slowing down until velocity reaches zero
Key terms in this question
scalar · vector · velocity · acceleration
Related
- All OCR A-Level Physics B: Advancing Physics (H557) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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