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Units of acceleration

AshPhys · Revision cheat sheet
AS Level9702 AS Ch.2Chapter 2: Accelerated motionLesson 2.3Sections 2.3

Goal: Explain why acceleration is in m s⁻², and convert other units to it.

01The big picture

Acceleration is a change in velocity (m s⁻¹) divided by a time (s), so its SI unit is metres per second per second: m s⁻² (also written m/s²).

An acceleration of 3 m s⁻² means the velocity grows by 3 m s⁻¹ every second. Before calculating, convert every quantity to SI units: km h⁻¹ to m s⁻¹ (divide by 3.6), minutes to seconds, cm to m.

m s⁻² [paraphrase]
Metres per second per second: the change in velocity, in m s⁻¹, each second.

02Key equations

The unit of a
m s−1s=m s−2\frac{\mathrm{m\,s^{-1}}}{\mathrm{s}} = \mathrm{m\,s^{-2}}
km h⁻¹ to m s⁻¹
1 km h−1=13.6 m s−11\ \mathrm{km\,h^{-1}} = \frac{1}{3.6}\ \mathrm{m\,s^{-1}}
Symbols and units
  • aaaccelerationm s−2\mathrm{m\,s^{-2}}
  • vvvelocitym s−1\mathrm{m\,s^{-1}}
  • tttimes\mathrm{s}

03Sample problems with solutions

Sample 1 · 0 to 100 km h⁻¹
A car accelerates from rest to 100 km h⁻¹ in 8.0 s. Calculate its average acceleration in m s⁻².

  1. Convert the velocity to m s⁻¹:

    v=1003.6=27.8 m s−1v = \frac{100}{3.6} = 27.8\ \mathrm{m\,s^{-1}}

  2. Divide by the time:

    a=27.8−08.0=3.47 m s−2a = \frac{27.8 - 0}{8.0} = 3.47\ \mathrm{m\,s^{-2}}
Answer: a=3.5 m s−2a = 3.5\ \mathrm{m\,s^{-2}} (2 s.f.)
Unit check: m s−1s=m s−2 ✓\frac{\mathrm{m\,s^{-1}}}{\mathrm{s}} = \mathrm{m\,s^{-2}}\ \checkmark

04Practice problems

  1. P1
    A motorbike goes from rest to 60 km h⁻¹ in 5.0 s. Find its acceleration.
    Final answer3.3 m s⁻²
    Answer: 3.3 m s⁻²
  2. P2
    A rocket’s speed rises by 30 m s⁻¹ every 2.0 s. Find its acceleration.
    Final answer15 m s⁻²
    Answer: 15 m s⁻²
  3. P3
    Express 1.2 cm s⁻² in m s⁻².
    Final answer0.012 m s⁻²
    Answer: 0.012 m s⁻²
  4. P4
    A train slows from 72 km h⁻¹ to rest in 1.0 minute. Find its acceleration.
    Final answer−0.33 m s⁻²
    Answer: −0.33 m s⁻²

05Other useful information

Common mistakes

  • ✗ Wrong: Give acceleration in m s⁻¹.

    ✓ Right: m s⁻¹ is velocity; acceleration is m s⁻².

  • ✗ Wrong: Divide km h⁻¹ by seconds.

    ✓ Right: Convert to m s⁻¹ (÷ 3.6) and minutes to seconds first.

Exam tips

  • Write the unit at every step; a wrong unit shows a missed conversion.

What the syllabus asks

  • 9702 topic 2: define and use acceleration; SI units. Coursebook 2.3.

Explore: Practice questions for this lesson