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Learning objectives
Core idea
Key formulae
Worked examples
Explore the graph
Common mistakes
Exam tip
Guided practice
Practice questions
Challenge
Summary
Quick quiz
Same topic, different board
Past paper questions

LearnYMA01WME01 · Mechanics 1Kinematics of a particle in a straight lineConstant acceleration formulae (suvat)

Kinematics of a particle in a straight line · Subtopic 1 of 3

Constant Acceleration Formulae (suvat)

Five letters, five formulas. Write down $s$ , $u$ , $v$ , $a$ , $t$ , fill in the three you know and the one you want, then pick the formula without the letter you don't need. Every formula assumes the acceleration is constant.

Edexcel YMA01 WME01≈ 35 minRevision 5 · updated 2026-10-27

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Section 1 of 14

Learning objectives

List $s,u,v,a,t$ and choose the right formula.
Handle decelerations with a negative $a$ .
Solve journeys in several stages.
Solve problems where two objects meet or overtake.

Pause and think

A car goes from $10$ to $20$ m s⁻¹ in $5$ s at a steady rate. Its average speed must be?

Section 2 of 14

Core idea

Start hereStopping distance

A train at 20 m s $^{-1}$ needs to stop at a platform 400 m away. How hard must it brake, and how long will it take? Five variables, $s,u,v,a,t$ , linked by five equations: know three, find the rest.

The big idea

Constant acceleration only: $v=u+at$ , $s=\frac12(u+v)t$ , $s=ut+\frac12at^2$ , $s=vt-\frac12at^2$ , $v^2=u^2+2as$ .

1. Deriving from the v–t graph

v–t graph: gradient a, area s

t = 0.5

u=3

a=2

. The area is a trapezium:

s=\tfrac12(u+v)t

. Substituting

v=u+at

gives

s=ut+\tfrac12at^2

All five from a straight-line graph

$a=\frac{v-u}t\Rightarrow v=u+at$
Gradient of the line.
$s=\tfrac12(u+v)t$
Area of the trapezium.
$s=\tfrac12(u+u+at)t=ut+\tfrac12at^2$
Substitute $v$ .
$s=vt-\tfrac12at^2$
Substitute $u=v-at$ instead.
$s=\tfrac12(u+v)\cdot\frac{v-u}a\Rightarrow v^2=u^2+2as$
Eliminate $t$ ; difference of squares.

v^2=u^2+2as

$s$: displacement (m).
$u,v$: initial, final velocity (m s⁻¹).
$a$: acceleration (m s⁻²).
$t$: time (s).

2. Examples

Worked exampleThe train

From 20 m s $^{-1}$ to rest in 400 m. Deceleration and time?

Goal: $a$ , $t$ .
Strategy: Known $u,v,s$ : use $v^2=u^2+2as$ , then $v=u+at$ .

$0=400+800a\Rightarrow a=-0.5$
$v^2=u^2+2as$ .
$0=20-0.5t\Rightarrow t=40$
$v=u+at$ .

AnswerDeceleration

0.5

m s

^{-2}

;

40

✓ Check

s=\frac12(20+0)(40)=400

✓.

Worked exampleCatching up

A passes P at a constant 12 m s $^{-1}$ . 5 s later B leaves P from rest with $a=3$ . When does B catch A?

Goal: $t$ .
Strategy: Write both positions in terms of A's time $t$ ; set equal.

$s_A=12t,\quad s_B=\tfrac12(3)(t-5)^2$
B has been moving for $t-5$ s.
$1.5(t-5)^2=12t\Rightarrow t^2-18t+25=0$
Expand, divide by 1.5.
$t=9\pm\sqrt{56}$
Formula.
$t=16.5\text{ s}$
$9-\sqrt{56}=1.5<5$ : before B starts, reject.

Answer

16.5

s after A passes P.

✓ Check

s_A=198

;

s_B=1.5(11.48)^2=198

✓.

Common misconceptionNon-constant acceleration suvat is only valid if

a

is constant throughout the stage. Split journeys into stages.

Pause and think

From 5 m s $^{-1}$ with $a=2$ , distance in 4 s?

Summary

Five equations; pick by the missing variable.
Constant acceleration only.

suvat: Constant-acceleration equations.

HistoryGalileo's ramps. Around 1604 Galileo rolled balls down gently sloping ramps and timed them with a water clock. He found distance grows with the square of time,

s\propto t^2

, the first experimental evidence for

s=\tfrac12at^2

Fun factCheetahs versus sports cars. A cheetah can reach about

25

m s⁻¹ in around

3

s, an average acceleration of roughly

8

m s⁻², comparable to a supercar. But it can only keep up its top speed for a few hundred metres.

Section 3 of 14

Key formulae

No s

v=u+at

No a

s=\tfrac12(u+v)t

No v

s=ut+\tfrac12at^2

No u

s=vt-\tfrac12at^2

No t

v^2=u^2+2as

TrickWrite the suvat list every time. Start every question with a five-line list:

s=\

u=\

v=\

a=\

t=\

. Fill in what you know, put a ? by what you want and a ✗ by what you don't care about. The ✗ chooses the formula for you.

Section 4 of 14

Worked examples

Example 1 · Braking distance0 / 2 steps

A cyclist at

20

m s⁻¹ decelerates at

2.5

m s⁻² until she stops. How far does she travel?

Example 2 · Catching up0 / 2 steps

Car

A

starts from rest with

a=2

m s⁻². Car

B

24

m ahead, moving at a steady

5

m s⁻¹. When does

A

catch

B

Section 5 of 14

Explore the graph

Velocity–time line and its area

Loading the interactive graph…

Try this

The line is $v=u+at$ for $5$ s; the shaded area is the displacement. The value is $s=5u+\tfrac12a(25)$ .
Check: with $u=4$ , $a=2$ the area is a trapezium with parallel sides $4$ and $14$ .
Make $a$ negative. What does the graph mean when it goes below the axis?

$s=ut+\tfrac12at^2$ is just the area under the velocity–time line.

In the real worldSpeed humps and stopping distances. The Highway Code's stopping distances (for example, about

23

m at

30

mph) come from reaction distance plus a braking distance calculated with

v^2=u^2+2as

Section 6 of 14

Common mistakes

IncorrectDeceleration

2.5

used as

a=+2.5

Correct

a=-2.5

It acts against the motion.

Incorrect

s=\tfrac12at^2

when

u\ne0

Correct

s=ut+\tfrac12at^2

Only start from rest drops the

ut

IncorrectMixing km h⁻¹ and m

CorrectConvert to m s⁻¹

SI units throughout.

IncorrectUsing suvat when acceleration changes

CorrectSplit into stages

Each stage needs constant

a

Use $v=u+at$ for everything
Write down $s, u, v, a, t$
Find the variable you don't know and don't need, pick the equation without it

Section 7 of 14

Exam tip

Exam tipState the formula. Write the formula before substituting (e.g. "

v^2=u^2+2as

"). A correct formula with correct values is the M1; a slip later only costs the A1.

Section 8 of 14

Guided practice

SA-IAL-M1-KM-G012 marksL1 FoundationCalculatorsuvat

A car moving at

4\ \text{m s}^{-1}

accelerates uniformly at

2\ \text{m s}^{-2}

for

5

s. Find its final speed.

Salam Academy Original Practice · Proposed mark scheme

Section 9 of 14

Practice questions

SA-IAL-M1-KM1-0022 marksL1 FoundationNon-calculatorsuvat

A particle speeds up from

5

m s⁻¹ to

17

m s⁻¹ with acceleration

3

m s⁻². How long does this take?

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-M1-KM-0022 marksL1 FoundationCalculatorsuvat

A particle starts from rest and accelerates uniformly at

1.5\ \text{m s}^{-2}

for

8

s. Find the distance travelled.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-M1-KM1-0032 marksL1 FoundationNon-calculatorsuvat

A particle's speed increases uniformly from

2

m s⁻¹ to

8

m s⁻¹ in

5

s. Find the distance travelled.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-M1-KM-0013 marksL1 FoundationCalculatorsuvat

A cyclist moving at

20\ \text{m s}^{-1}

brakes with constant deceleration

2.5\ \text{m s}^{-2}

until she stops. Find the distance she travels while braking.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-M1-KM1-0042 marksL2 StandardNon-calculatorsuvat

A particle moving at

10

m s⁻¹ comes to rest in

25

m with constant acceleration. Find the acceleration.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-M1-KM1-0052 marksL2 StandardNon-calculatorsuvat

A particle has initial velocity

6

m s⁻¹ and acceleration

-2

m s⁻². Find its displacement after

4

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-M1-KM-0082 marksL2 StandardCalculatorsuvat

A particle accelerates uniformly at

2\ \text{m s}^{-2}

and reaches

10\ \text{m s}^{-1}

after

4

s. Find its displacement during these

4

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-M1-KM1-0063 marksL2 StandardNon-calculatorStages & meetings

A car starts from rest and accelerates at

2

m s⁻² for

5

s, then travels at constant speed for

10

s. Find the total distance.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-M1-KM-0094 marksL3 ExamCalculatorStages & meetings

Car

A

starts from rest at a junction and accelerates at

2\ \text{m s}^{-2}

. At the same moment, car

B

passes the junction at a constant

6\ \text{m s}^{-1}

in the same direction. Find the time when

A

catches

B

Salam Academy Original Practice · Proposed mark scheme

More questions on every skill in this subtopic are in the question bank under Practise.

Section 10 of 14

Challenge

SA-IAL-M1-KM1-0074 marksL3 ExamNon-calculatorStages & meetings

Car

A

starts from rest with acceleration

2

m s⁻². At the same moment car

B

24

m ahead on the same road, is moving at a constant

5

m s⁻¹ in the same direction. Find the time when

A

catches

B

Salam Academy Original Practice · Proposed mark scheme

Section 11 of 14

Summary

List $s,u,v,a,t$ ; drop the letter you don't need.
Deceleration: negative $a$ .
Stages: $v$ of one stage is $u$ of the next.
Two objects: same $t$ , equal positions.

Section 12 of 14

Quick quiz

Q1 · SA-IAL-M1-KM1-0012 marksL1 FoundationNon-calculatorsuvat

A particle moving at

3

m s⁻¹ accelerates at

2

m s⁻² over a distance of

10

m. Find its final speed.

Salam Academy Original Practice · Proposed mark scheme

Section 13 of 14

Same topic, different board

Specification: IAL Mathematics, unit WME01 (Mechanics 1)
Where: M1 · 3 Kinematics of a particle moving in a straight line
Expected: Use the five constant acceleration formulae, including for journeys in several stages and problems with two particles.
Calculator: Calculators are permitted, but exact answers (surds, fractions, π) are expected where the question asks.
Typical style: Two-part questions: "find the acceleration" then "find the distance travelled in the first T seconds".
Open in: YMA01 · WME01

Section 14 of 14

Past paper questions

2 questions (23 marks) from real exams test this subtopic. Try each one under timed conditions, then mark it with the official mark scheme.

WME01/01 · January 2025Question 211 marks
Speed–time graph for a motorbike that speeds up and slows down.
Question paper, page 4 Mark scheme
WME01/01 · June 2024Question 612 marks
Friction and resolving at constant speed, then deceleration and distance.
Question paper, page 16 Mark scheme

All YMA01 past paper questions by topic

Salam Academy original content · Content status: reviewed and published. Syllabus mapping: Pearson Edexcel YMA01, 2018 specification (official specification).