Pearson Edexcel · A-Level · Mathematics
Course version: 9MA0 · Version from Mar 2026
Understand and use fundamental quantities and units in the S.I. system:…
Full specification wording
Quantities and units in mechanics: 6.1 Understand and use fundamental quantities and units in the S.I. system: length, time, mass. Understand and use derived quantities and units: velocity, acceleration, force, weight, moment.
Mechanics begins with three fundamental S.I. quantities: length measured in metres (m), time in seconds (s) and mass in kilograms (kg).
Checked against the Pearson Edexcel 9MA0 specification (opens in a new tab) on .
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Mechanics begins with three fundamental S.I. quantities: length measured in metres (m), time in seconds (s) and mass in kilograms (kg). Derived quantities are formed by combining these. Velocity is displacement per unit time, with unit m s⁻¹; acceleration is velocity change per unit time, with unit m s⁻². Force is mass times acceleration, so its unit is kg m s⁻², named the newton (N). Weight is the force of gravity on a mass, W = mg, also measured in newtons, where g is about 9.8 m s⁻² near the Earth's surface. Moment is the turning effect of a force about a point, defined as force times perpendicular distance, with unit N m. Checking that every term in an equation has consistent units is a powerful way to detect errors.
What earns the marks
- State the fundamental S.I. quantities as length, time and mass with units m, s and kg respectively.
- Derive the unit of velocity as m s⁻¹ and acceleration as m s⁻² from their definitions as rates of change.
- Show that force has unit kg m s⁻², equivalent to the newton, from F = ma.
- Distinguish weight as a force, W = mg, measured in newtons, from mass measured in kilograms.
- Define moment as force multiplied by perpendicular distance and give its unit as N m.
Common mistakes and how to put them right
Treating weight and mass as the same quantity.
Put it right: Mass is in kg while weight is a force in N given by W = mg.
Writing the unit of force as kg m s⁻¹.
Put it right: The corrected unit is kg m s⁻², since acceleration is m s⁻².
Using the distance along the line of action rather than the perpendicular distance when computing a moment.
Put it right: The corrected method uses the perpendicular distance from the pivot.
Exam tips
- Carry units through every line of working so inconsistencies are visible immediately.
- Convert grams to kilograms and centimetres to metres before substituting into formulae.
- When asked to distinguish quantities, name the quantity, its symbol, its unit and whether it is scalar or vector.
Try the lesson
The start of the Quantities and units in mechanics: 6.1 Understand and use fundamental quantities and units in the S.I. system: length, time, mass. Understand and use derived quantities and units: velocity, acceleration, force, weight, moment. lesson, made from checked teaching notes for this specification point.
Have a go first
A trolley accelerates uniformly from rest at 3 m s⁻². Which of the following correctly gives the S.I. base units of the acceleration and identifies acceleration as a derived quantity?
Listen
Mechanics begins with three fundamental S.I. quantities: length measured in metres (m), time in seconds (s) and mass in kilograms (kg). Derived quantities are formed by combining these. Velocity is displacement per unit time, with unit m s⁻¹; acceleration is velocity change per unit time, with unit m s⁻². Force is mass times acceleration, so its unit is kg m s⁻², named the newton (N). Weight is the force of gravity on a mass, W = mg, also measured in newtons, where g is about 9.8 m s⁻² near the Earth's surface. Moment is the turning effect of a force about a point, defined as force times perpendicular distance, with unit N m. Checking that every term in an equation has consistent units is a powerful way to detect errors. A strong answer earns marks for these points. State the fundamental S.I. quantities as length, time and mass with units m, s and kg respectively. Derive the unit of velocity as m s⁻¹ and acceleration as m s⁻² from their definitions as rates of change. Show that force has unit kg m s⁻², equivalent to the newton, from F = ma. Distinguish weight as a force, W = mg, measured in newtons, from mass measured in kilograms. A common slip: Treating weight and mass as the same quantity. Instead, mass is in kg while weight is a force in N given by W = mg. Exam tip: Carry units through every line of working so inconsistencies are visible immediately.
Key words
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Fundamental S.I. quantities
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Derived units and dimensional consistency
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Weight as a force
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Moment and perpendicular distance
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See every definition
- Fundamental S.I. quantities
- Length measured in metres, time in seconds and mass in kilograms, the three quantities from which derived quantities are formed.
- Derived units and dimensional consistency
- Quantities formed by combining the fundamental ones, and checking that every term in an equation has consistent units to detect errors.
- Weight as a force
- The force of gravity on a mass, W = mg, measured in newtons, where g is about 9.8 m s⁻² near the Earth's surface.
- Moment and perpendicular distance
- The turning effect of a force about a point, defined as force times perpendicular distance, with unit N m.
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