A student measures the length of a piece of string using a ruler. Another student then measures the speed of a toy car as it rolls across a floor, timing it with a stopwatch over a measured distance. Explain the difference between a scalar quantity and a vector quantity, and for each measurement taken by the students — length, distance, time and speed — state whether it is a scalar or a vector quantity, justifying your answer.

OCR A-Level Physics A (H556) — 2.1 Physical quantities and units · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

In physics, all measured quantities can be classified as either scalar or vector quantities. Understanding this distinction is fundamental to describing motion correctly.

Model answer (5 marks)

A scalar quantity is a physical quantity that is completely described by a magnitude alone; it has no associated direction.
A vector quantity is described by both a magnitude and a direction.
Length – scalar: it is the size of an object, no direction required.
Distance – scalar: it is the total path travelled, no direction.
Time – scalar: it is an amount of duration, no direction.
Speed – scalar: it is the rate of motion, no direction (velocity would be the vector form).

Examiner tips

  • Use the definition of scalar and vector first, then classify each quantity with a brief justification.
  • Remember that speed is scalar; velocity is the vector equivalent.
  • Keep the answer concise – 5 marks can be earned with 5 short statements.

Common mistakes

  • Confusing speed with velocity and marking speed as a vector.
  • Including unnecessary detail such as units or measurement methods.
  • Failing to state the direction component (or lack thereof) for each quantity.

Mark scheme (5 marks)

  1. A scalar quantity has magnitude only (and no direction).
  2. A vector quantity has both magnitude and direction.
  3. Length and distance are scalar quantities because they only measure how far an object has moved/how long something is, with no direction needed.
  4. Time is a scalar quantity because it has magnitude (an amount) but no direction.
  5. Speed is a scalar quantity because it describes how fast an object moves but does not include direction; velocity (not speed) is the vector equivalent as it gives speed in a given direction.

Key terms in this question

scalar · vector · distance · speed

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