S.I. units: (m), time

The idea

This row completes the base-unit list: length has the base unit metre (m), and time is the next S.I. base quantity, with the base unit second (s). Time measures duration and appears in derived quantities such as speed (m s⁻¹), acceleration (m s⁻²) and frequency (s⁻¹ or Hz). In calculations, convert minutes to seconds by multiplying by 60, so 2.5 min = 150 s, and convert milliseconds by multiplying by 10⁻³, so 50 ms = 0.050 s. The second is defined from atomic transitions, but for A Level you simply treat it as the base unit of time.

What earns the marks

• Identifies time as an S.I. base quantity with base unit the second (s).
• Links the metre (m) to length and the second (s) to time as base units.
• Converts times from minutes or milliseconds to seconds before substituting into equations.
• Recognises derived units involving time, such as m s⁻¹ for speed and s⁻¹ for frequency.

Common mistakes and how to put them right

• Treating the minute as the base unit.

  Put it right: The base unit of time is the second (s).

• Substituting minutes directly into an equation.

  Put it right: Multiply by 60 to obtain seconds first.

• Writing speed as m/s with a solidus in a multi-unit expression.

  Put it right: Use negative indices such as m s⁻¹.

Exam tips

• Convert all times to seconds before substituting into an equation.
• Write compound units with negative indices, for example m s⁻¹ and m s⁻².
• Check that a frequency answer is in s⁻¹ or Hz and not confused with a period in s.