AQA · A-Level · Physical Education
Course version: 7582 · Version from Sept 2016
Definitions, equations and units of example scalars.
Full specification wording
Biomechanical principles: Definitions, equations and units of example scalars.
A scalar is a quantity with magnitude (size) only and no direction, unlike a vector which has both magnitude and direction.
Checked against the AQA 7582 specification (opens in a new tab) on .
- Point 3 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A scalar is a quantity with magnitude (size) only and no direction, unlike a vector which has both magnitude and direction. Example scalars in biomechanics include distance, speed, mass, time and energy. Distance is how far a performer travels along a path, measured in metres (m); speed is distance divided by time, speed = distance ÷ time, measured in metres per second (m/s); mass is the amount of matter in a body, measured in kilograms (kg); time is measured in seconds (s); and energy is measured in joules (J). Because scalars have no direction, a 400 m runner who returns to the start has covered a distance of 400 m even though displacement is zero.
What earns the marks
- A scalar is a quantity with magnitude only and no direction, whereas a vector has both magnitude and direction.
- Distance is the total length of the path travelled, measured in metres (m).
- Speed is the rate of change of distance, given by speed = distance ÷ time, measured in metres per second (m/s).
- Mass is the quantity of matter in a body, measured in kilograms (kg), and time is measured in seconds (s).
- Energy is a scalar measured in joules (J), and recognising which quantities are scalars helps select the correct equation and unit.
Common mistakes and how to put them right
Treating speed as a vector.
Put it right: Speed is a scalar with magnitude only, while velocity is the vector that also states direction.
Using the wrong unit for a scalar, such as giving speed in metres.
Put it right: Speed is measured in metres per second (m/s).
Confusing distance with displacement.
Put it right: Distance is a scalar path length in metres, while displacement is a vector with direction.
Rearranging speed = distance ÷ time incorrectly, for example multiplying distance by time.
Put it right: Divide distance by time to find speed.
Exam tips
- Identify whether the quantity in the stem is a scalar or a vector before selecting an option, since direction is the deciding feature.
- Match each scalar to its unit: distance in metres (m), speed in metres per second (m/s), mass in kilograms (kg), time in seconds (s) and energy in joules (J).
- For any calculation, write the equation first, such as speed = distance ÷ time, then substitute the values with units.
- Check that your answer's unit matches the quantity asked for, because a correct number with the wrong unit is still wrong.
Try the lesson
The start of the Biomechanical principles: Definitions, equations and units of example scalars. lesson, made from checked teaching notes for this specification point.
Have a go first
Which of the following quantities is a scalar, meaning it is fully described by magnitude alone with no direction?
Listen
A scalar is a quantity with magnitude (size) only and no direction, unlike a vector which has both magnitude and direction. Example scalars in biomechanics include distance, speed, mass, time and energy. Distance is how far a performer travels along a path, measured in metres (m); speed is distance divided by time, speed = distance ÷ time, measured in metres per second (m/s); mass is the amount of matter in a body, measured in kilograms (kg); time is measured in seconds (s); and energy is measured in joules (J). Because scalars have no direction, a 400 m runner who returns to the start has covered a distance of 400 m even though displacement is zero. A strong answer earns marks for these points. A scalar is a quantity with magnitude only and no direction, whereas a vector has both magnitude and direction. Distance is the total length of the path travelled, measured in metres (m). Speed is the rate of change of distance, given by speed = distance ÷ time, measured in metres per second (m/s). Mass is the quantity of matter in a body, measured in kilograms (kg), and time is measured in seconds (s). A common slip: Treating speed as a vector. Instead, speed is a scalar with magnitude only, while velocity is the vector that also states direction. Exam tip: Identify whether the quantity in the stem is a scalar or a vector before selecting an option, since direction is the deciding feature.
See it
Key words
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Scalar
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Distance
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Speed
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Mass
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See every definition
- Scalar
- A quantity with magnitude (size) only and no direction, unlike a vector which has both magnitude and direction.
- Distance
- How far a performer travels along a path, measured in metres (m).
- Speed
- Distance divided by time, speed = distance ÷ time, measured in metres per second (m/s).
- Mass
- The amount of matter in a body, measured in kilograms (kg).
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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