AQA · GCSE · Physics
Course version: 8463 · Version from Sept 2016
Students should be able to explain the vector–scalar distinction as it…
Full specification wording
Velocity: Students should be able to explain the vector–scalar distinction as it applies to displacement, distance, velocity and speed.
Set the four quantities out in pairs.
Checked against the AQA 8463 specification (opens in a new tab) on .
- Point 2 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Set the four quantities out in pairs. Distance and speed are scalars, with magnitude only and no direction. Displacement and velocity are their vector partners, carrying magnitude and direction. The pairs connect through time, since speed is distance over time and velocity is displacement over time, so the scalar or vector nature carries through the division. A train taking a curved route travels a distance of, say, 12 km along the track but is displaced only 8.5 km in a straight line; over 600 s its average speed is 20 m/s while its average velocity is about 14 m/s in the direction from the first station to the second. Any journey returning to its start has zero displacement and zero average velocity, though neither its distance nor its average speed is zero.
What earns the marks
- Distance and speed identified as scalars with magnitude only.
- Displacement and velocity identified as vectors with magnitude and direction.
- Pairing each scalar with its vector partner.
- A worked comparison showing the two differing on a curved route.
Common mistakes and how to put them right
Pairing displacement with speed, or distance with velocity.
Claiming displacement and distance are always equal.
Saying the average velocity of a round trip equals its average speed.
Defining a vector as a bigger quantity rather than as one with direction.
Exam tips
- Learn the four as two pairs, with the vector always carrying the direction.
- For a closed loop, write zero displacement and zero average velocity immediately.
Try the lesson
The start of the Velocity: Students should be able to explain the vector–scalar distinction as it applies to displacement, distance, velocity and speed. lesson, made from checked teaching notes for this specification point.
Have a go first
Which of these quantities is a vector quantity?
Listen
Set the four quantities out in pairs. Distance and speed are scalars, with magnitude only and no direction. Displacement and velocity are their vector partners, carrying magnitude and direction. The pairs connect through time, since speed is distance over time and velocity is displacement over time, so the scalar or vector nature carries through the division. A train taking a curved route travels a distance of, say, 12 km along the track but is displaced only 8.5 km in a straight line; over 600 s its average speed is 20 m/s while its average velocity is about 14 m/s in the direction from the first station to the second. Any journey returning to its start has zero displacement and zero average velocity, though neither its distance nor its average speed is zero. A strong answer earns marks for these points. distance and speed identified as scalars with magnitude only. displacement and velocity identified as vectors with magnitude and direction. pairing each scalar with its vector partner. a worked comparison showing the two differing on a curved route. Exam tip: Learn the four as two pairs, with the vector always carrying the direction.
Key words
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scalars
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vectors
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displacement
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average velocity
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See every definition
- scalars
- Quantities such as distance and speed that have magnitude only and no direction.
- vectors
- Quantities such as displacement and velocity that carry magnitude and direction.
- displacement
- The vector partner of distance, carrying magnitude and direction, and zero for any journey returning to its start.
- average velocity
- Displacement over time, which is zero for a journey returning to its start.
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