Units for motion and force, and setting out a calculation
A number on its own tells you nothing in physics.
"Speed 3" could mean 3 m/s (a brisk walk) or 3 km/s (faster than a rifle bullet).
The unit is part of the answer.
This section gives you the units for the whole of Forces and motion, the prefixes you must convert, and the way to set out a calculation so that every step can earn a mark.
The units you need
You need to use these units: kilogram (kg), metre (m), metre/second (m/s), metre/second² (m/s²), newton (N), second (s) and newton/kilogram (N/kg).
Quantity
Unit
Symbol
mass
kilogram
kg
distance, length, height
metre
m
time
second
s
speed and velocity
metre/second
m/s
acceleration
metre/second²
m/s²
force (including weight and friction)
newton
N
gravitational field strength
newton/kilogram
N/kg
Each unit tells you what the quantity means:
- m/s is metres travelled in each second.
- m/s² is "metres per second, per second". Acceleration is how much the velocity changes in each second. A car with an acceleration of 3 m/s² gains 3 m/s of speed every second.
- N/kg is newtons of weight on each kilogram. On Earth, g = 10 N/kg, so each kilogram is pulled down with a force of 10 N.
The page of formulae printed in each paper says "g = 10 m/s²".
That is the same number with a different unit.
Why it works (not examined): one newton is the force that gives 1 kg an acceleration of 1 m/s², so a newton per kilogram is the same as a metre per second².
Prefixes and time conversions
Equations in this unit only work with the units in the table.
A mass in grams or a time in minutes must be converted first.
None of these factors is printed in the paper, so learn them.
Prefix or unit
Meaning
To convert to the base unit
k (kilo)
× 1000
2.5 km = 2500 m
M (mega)
× 1 000 000
3 MN = 3 000 000 N
c (centi)
÷ 100
45 cm = 0.45 m
m (milli)
÷ 1000
250 g = 0.250 kg; 350 mN = 0.350 N; 20 ms = 0.020 s
minute
60 s
2.5 minutes = 150 s
hour
3600 s
1.5 hours = 5400 s
km/h
÷ 3.6 to get m/s
72 km/h = 20 m/s
The kilogram is the odd one out: its base unit already has a prefix.
So grams go down by 1000 to become kilograms.
A 250 g ball has a mass of 0.25 kg, never 250 000 kg.
Why ÷ 3.6 works: 1 km/h is 1000 m in 3600 s, which is m/s.
Where the equations of this unit are printed
Each of the eight papers set from November 2023 to June 2025 had a FORMULAE page on page 2 and an Equation Booklet enclosed with it.
The relationships you must "know and use" are still treated as recall: questions often begin "State the formula linking ..."
for 1 mark.
Learn every one.
Relationship
Where it is printed
What you must do
average speed = distance moved ÷ time taken
Equation Booklet
recall and use
acceleration = change in velocity ÷ time taken
Equation Booklet
recall and use
force = mass × acceleration
Equation Booklet
recall and use
weight = mass × gravitational field strength
Equation Booklet
recall and use
momentum = mass × velocity (Paper 2)
Equation Booklet
recall and use
moment = force × perpendicular distance from the pivot (Paper 2)
Equation Booklet
recall and use
(final speed)² = (initial speed)² + (2 × acceleration × distance moved)
FORMULAE page, both papers
use, and know when it applies
force = change in momentum ÷ time taken (Paper 2)
FORMULAE page, Paper 2
use, and know when it applies
g = 10 m/s²
FORMULAE page
use in every calculation
Setting out a calculation
Mark schemes give marks for steps, not only for the final number.
Write one line for each step:
1. the equation, in words or symbols;
2. any unit conversion (cm to m, g to kg, minutes to s);
3. the substitution: put the numbers into the equation before you move anything;
4. the rearrangement, if the unknown is not already the subject;
5. the evaluation: work out the number;
6. the answer with its unit, usually to 2 or 3 significant figures.
Two rules come from how the marks are given:
- Substitute first. If you rearrange wrongly and then substitute, you can score nothing. If you substitute first and then rearrange wrongly, the substitution mark is already yours.
- A power-of-ten slip costs one mark. Forgetting to change 250 g into 0.25 kg makes the answer 1000 times too big, and you lose the evaluation mark. One slip, one mark.
The unit is usually printed on the answer line, and then it earns no mark of its own.
When a question asks you to "give a suitable unit", the unit is a mark.
Significant figures earn a mark only when the question names them ("Give your answer to 2 significant figures").
- Newton (N): the unit of force.
- Gravitational field strength (g): the force of gravity on each kilogram, in N/kg; 10 N/kg near the Earth's surface.
- Substitution: writing the numbers, in the correct units, into an equation.
Convert each value to the unit used in the equations: a 250 g ball; a 45 cm ramp; 2.5 minutes; 72 km/h.
1. kg (grams to kilograms: divide by 1000)
2. m (centimetres to metres: divide by 100)
3. s (minutes to seconds: multiply by 60)
4. m/s (km/h to m/s: divide by 3.6)
Answer: 0.25 kg, 0.45 m, 150 s, 20 m/s.
A tram travels 1.2 km between two stops in 2.5 minutes.
Calculate its average speed.
1. average speed = distance moved ÷ time taken
2. 1.2 km = 1200 m and 2.5 minutes = 150 s (1) conversion
3. average speed = 1200 ÷ 150 (1) substitution
4. average speed = 8.0 m/s (1) evaluation
Answer: 8.0 m/s.
Leaving the time in minutes gives 480, which is wrong by a factor of 60.
A train has an average speed of 24 m/s.
Calculate the time it takes to travel 3.6 km.
1. average speed = distance moved ÷ time taken
2. 3.6 km = 3600 m conversion
3. (1) substitution
4. (1) rearrangement
5. s (1) evaluation
Answer: 150 s (2.5 minutes).
A student who forgets the kilometre and writes s still keeps the substitution and rearrangement marks: one power-of-ten slip costs one mark.
A garden snail crawls 0.84 m in 35 s.
Calculate its average speed.
Give your answer in standard form to 2 significant figures.
1. average speed = 0.84 ÷ 35 (1) substitution
2. average speed = 0.024 m/s (1) evaluation
3. m/s (1) standard form, 2 significant figures
Answer: m/s.
Standard form keeps the zeros under control: the "×10" button on a calculator stops you typing an extra zero.
Before you write any equation, scan the question for prefixes and time units (g, cm, km, mN, ms, minutes, hours) and convert them on their own line.
All four recent examiners' reports on each paper named unconverted units as the commonest way to lose a calculation mark.
- Grams the wrong way. 0.5 kg is 500 g, so 500 g is 0.5 kg. Multiplying by 1000 instead of dividing gives an answer a million times too big. Ask: "is a gram bigger or smaller than a kilogram?"
- Rearranging first. Writing straight away scores 0. Writing first scores 1 even if the next line goes wrong.
- Rounding too early. Keep all the figures on your calculator until the last line, then round. Rounding a middle value to 1 significant figure can push the answer outside the accepted range.
- Missing units in a "give a suitable unit" question. If the question asks for the unit, a bare number loses that mark.
Check your understanding
1. Which of these is the unit of gravitational field strength?
- A N
- B N/kg
- C kg/N
- D kg m/s
(1) Total [1]
2. Complete the table by giving the unit and its symbol for each quantity.
Quantity
Unit
Symbol
mass
force
acceleration
(3) Total [3]
3. A student measures the speed of a snail as 1.5 mm/s. Give this speed in m/s, in standard form. (2) Total [2]
4. Show that 90 km/h is 25 m/s. (2) Total [2]
5. A student answers a 3-mark speed question by writing the equation, then rearranging it, then substituting. Her rearrangement is wrong. Explain why she would have scored more marks if she had substituted before rearranging. (2) Total [2]
Answers
1. B (1). A is the unit of force, not force per kilogram. C is upside down. D is the unit of momentum.
2. kilogram, kg (1); newton, N (1); metre/second², m/s² (1).
3. 1.5 mm/s = 1.5 ÷ 1000 = 0.0015 m/s (1); m/s (1).
4. 90 km = 90 000 m and 1 hour = 3600 s (1); 90 000 ÷ 3600 = 25 m/s, shown in full (1). (90 ÷ 3.6 = 25 also scores both marks.)
5. A correct substitution line earns a mark by itself (1); a wrong rearrangement written first scores nothing, but after a correct substitution it loses only the later marks (1).