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AS & A-Level Physics 02 — Describing Motion

AS & A-Level Physics 02 — Describing Motion

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 2 of 26: Describing motion. Concepts, worked applications and misconception checks.

Physics EN AS & A-Level
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Scalars and Vectors in Motion

In physics, describing motion requires distinguishing between scalar and vector quantities. A scalar has only magnitude (a size or amount), whereas a vector has both magnitude and direction. Distance is a scalar representing the total length of the path travelled, like the reading on a car's odometer. Displacement, however, is a vector; it is the straight-line change in position from the start point to the end point, including the direction. Similarly, speed is the scalar rate of change of distance, while velocity is the vector rate of change of displacement. An object can have a constant speed while its velocity changes, for example, when moving in a circle. Acceleration is also a vector, defined as the rate at which an object's velocity changes. This change can be in speed, direction, or both.

Key points

  • Distance is a scalar (total path length); Displacement is a vector (change in position with direction).
  • Speed is a scalar (rate of change of distance); Velocity is a vector (rate of change of displacement).
  • Acceleration is a vector, defined as the rate of change of velocity (a=Δv/Δta = \Delta v / \Delta t).
  • Average speed = total distance / time taken. Average velocity = total displacement / time taken.

Worked example

Question

A delivery drone flies 300 m North, then 400 m East. The journey takes 50 s. Calculate its average speed and the magnitude of its average velocity.

Solution

1. Calculate the total distance travelled: d=300 m+400 m=700 md = 300 \text{ m} + 400 \text{ m} = 700 \text{ m}.
2. Calculate the average speed: Average speed = distance / time = 700 m/50 s=14 m/s700 \text{ m} / 50 \text{ s} = 14 \text{ m/s}.
3. The displacement is the hypotenuse of the right-angled triangle formed by the drone's path. Use Pythagoras' theorem: s=3002+4002=90000+160000=250000=500 ms = \sqrt{300^2 + 400^2} = \sqrt{90000 + 160000} = \sqrt{250000} = 500 \text{ m}.
4. Calculate the magnitude of the average velocity: Average velocity magnitude = displacement / time = 500 m/50 s=10 m/s500 \text{ m} / 50 \text{ s} = 10 \text{ m/s}.

The drone's average speed is 14 m/s, and the magnitude of its average velocity is 10 m/s.

Common pitfalls

  • Confusing speed with velocity. A car driving in a circle at a constant speed has a constantly changing velocity because its direction is changing. Therefore, it is accelerating.
  • Assuming distance and displacement are always the same. They are only equal if the object moves in a straight line without changing direction.

Prerequisites

  • Understanding the fundamental difference between scalar and vector quantities is essential for all definitions in this concept.
  • Basic calculations are required for the worked example.
Further resources