Where can I learn Equations of motion for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 2.1 (Equations of motion) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/2-1-equations-of-motion.

Is Equations of motion (2.1) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Equations of motion.

How do I revise Equations of motion for 9702 exams?

Start with the visual steps on this page, note the key exam points, then attempt a 9702 past-paper question on Equations of motion using MarkScheme's /mark tool. Mark strictly against the official scheme and re-read any marks you lost.

MarkScheme 9702

Opening…

2.1Physics25 min readPREMIUM

Equations of motion

Welcome to kinematics, the study of motion without worrying about the forces causing it! This lesson will equip you with the essential tools to describe and predict how objects move, especially under uniform acceleration. You'll master key terms, learn powerful equations, and understand how graphs visually represent motion. This pilot aligns with Senpai Corner AS notes (2025–2027) for topic 2.1.

BY THE END, YOU CAN…

exam checklist — tick these off

1Apply SUVAT equations to solve problems involving uniform acceleration.
2Interpret and draw displacement-time and velocity-time graphs, calculating gradient and area.
3Analyse projectile motion by resolving it into independent horizontal and vertical components.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Equations of motion

Cambridge 9702 Paper 2 — Equations of motion (2.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
Speed is the total distance travelled per unit time (a scalar quantity).
2
Velocity is the rate of change of displacement (a vector quantity). The sign (+ or -) indicates direction.
3
Acceleration is the rate of change of velocity (a vector quantity).
4
Example: If 'up' is the positive direction, an object moving upwards at 5 m/s has a velocity of +5 m/s. An object moving downwards at 5 m/s has a velocity of -5 m/s. Both have a speed of 5 m/s.

What this topic covers

The official Cambridge syllabus points this lesson works through.

2.1.1
Define and use distance, displacement, speed, velocity and acceleration
2.1.2
Use graphical methods to represent distance, displacement, speed, velocity and acceleration
2.1.3
Determine displacement from the area under a velocity-time graph
2.1.4
Determine velocity using the gradient of a displacement-time graph
2.1.5
Determine acceleration using the gradient of a velocity-time graph
2.1.6
Derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line
2.1.7
Solve problems using equations that represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance
2.1.8
Describe an experiment to determine the acceleration of free fall using a falling object
2.1.9
Describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Figure Interactive1 / 3

Trajectory Horizontal and vertical motion combine into a parabola; scrub time to fly it.

67 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

67 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

The Physics ClassroomStart here · 19702 2.1 · IB A.1
Kinematic Graphing
A moped leaves a trail of dots; set the initial velocity, acceleration and time and watch the position-, velocity- and acceleration-time graphs
Why this one: Set u, a and t for the moped and watch the dot spacing, the s–t curve and the v–t line grow together: SUVAT on screen.
Try this
1. Set the acceleration to zero and read the three graphs.
2. Add a positive acceleration and compare the dot spacing.
3. Give the initial velocity and acceleration opposite signs.
Look for The gradient of the position-time graph equals the value shown on the velocity-time graph.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN PhysicsStart here · 29702 2.1 · IB A.1
Linear Motion – Graphs of x, v, and a
Set velocity and acceleration for linear motion; read x-t, v-t and a-t graphs
Why this one: Constant a turns the x–t graph into a parabola and the v–t graph into a straight line of gradient a.
Try this
1. Set a velocity with zero acceleration and read the x-t graph.
2. Add a positive acceleration and compare the x-t and v-t graphs.
3. Set a negative acceleration and compare.
Look for Constant velocity gives a straight x-t line; constant acceleration gives a parabola in x-t and a straight v-t line.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 39702 2.1 · IB A.1
1D Kinematics: Velocity vs. Time Graph
Shape a straight-line v-t graph by dragging points; read off displacement, acceleration and motion
Why this one: Drag the v–t line and read displacement as the signed area and acceleration as the gradient.
Try this
1. Drag the points to make a constant positive velocity and read the displacement.
2. Make the line slope down through zero velocity.
3. Make the line steeper and read the acceleration.
Look for Displacement is the signed area under the v-t line and acceleration is its gradient.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
PhETStart here · 49702 2.1
Projectile Motion
Fire a cannon with chosen speed and angle; trace the path with or without air resistance.
Why this one: Switch on velocity vectors: the horizontal arrow never changes while the vertical one grows by g each second.
Try this
1. Set 15 m/s at 45° with air resistance off — note the range, then try 30° and 60°.
2. Fire horizontally from height; use the tape to check s = ½gt² for the drop.
3. Turn on velocity vectors — the horizontal arrow never changes.
Look for Horizontal velocity is constant; vertical motion is uniform acceleration g — equal ranges at complementary angles.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
The Physics ClassroomStart here · 59702 2.1 · IB A.1
Graph That Motion
Match 11 animated motions to their position-time and velocity-time graphs
Why this one: Match a moving object to its s–t and v–t graphs; a curving s–t pairs with a sloping v–t.
Try this
1. Watch a motion and choose its position-time graph.
2. Choose its velocity-time graph.
3. Check and move to the next motion.
Look for A curved position-time graph pairs with a sloping velocity-time graph.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

More simulations62 more on this topic — core ones first

PhETCoreJava · best on a laptop9702 2.1
The Moving Man
Drag the man along the line, or type in position, velocity and acceleration, and watch all three graphs update together.
Try this
1. Drag the man at a steady walk — the velocity graph is flat.
2. Set an acceleration and play — the position graph curves.
3. Walk left then right — note where velocity crosses zero.
Look for Gradient of x–t is v; gradient of v–t is a; turning points of x are where v = 0.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
oPhysicsCore9702 1.4 · 9702 2.1 · IB A.1
Relative Velocity: Boat Crossing a River
Set boat heading, boat speed and river speed; watch the resultant path across the river
Try this
1. Point the boat straight across with the river flowing and watch the path.
2. Angle the heading upstream until the path is straight across.
3. Set the river speed equal to the boat speed and try to cross directly.
Look for The boat’s path follows the vector sum of boat velocity and river velocity, so heading and path differ whenever the river flows.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 2.1 · IB A.1
Uniform Acceleration in One Dimension: Motion Graphs
Adjust initial position, velocity and acceleration; watch the motion and its x-t, v-t, a-t graphs together
Try this
1. Set acceleration to zero and a positive initial velocity; compare the three graphs.
2. Give a positive initial velocity and a negative acceleration.
3. Set initial velocity to zero and vary only the acceleration.
Look for The v-t gradient equals the a-t value and the x-t gradient equals the v-t value, so a straight v-t line pairs with a parabolic x-t curve.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 2.1 · IB A.1
Position, Velocity, and Acceleration vs. Time Graphs
Slide points on a v-t graph; the x-t and a-t graphs update to match the motion
Try this
1. Slide the v-t points to make a horizontal line and look at the x-t graph.
2. Make the v-t line slope upward through zero.
3. Make a v-t segment slope downward and check the sign on the a-t graph.
Look for Where the v-t line crosses zero the x-t graph turns around, and the a-t value is the v-t gradient.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 2.1 · IB A.1
Kinematics Graphs: Adjust the Acceleration
Set initial position/velocity then adjust acceleration; see x-t, v-t and a-t graphs of the object
Try this
1. Set initial velocity positive and acceleration zero, then run.
2. Keep the same initial velocity and set a negative acceleration.
3. Double the acceleration and compare the v-t slopes.
Look for Doubling the acceleration doubles the v-t gradient and makes the x-t parabola curve more tightly.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 2.1 · IB A.1
Uniform Acceleration in One Dimension
Adjust x0, v0 and a for a car under uniform acceleration; run and watch the resulting motion and data
Try this
1. Set v0 positive and a = 0, then run.
2. Set v0 positive and a negative, run, and watch the car reverse.
3. Set v0 = 0 and compare runs at two values of a.
Look for With v0 and a of opposite sign the car slows, stops momentarily and returns; the data follow v = v0 + at.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$v = \frac{\Delta s}{\Delta t}$

Tap a symbol — great for exam definitions

KEY RELATION

= u + at

Tap a symbol — great for exam definitions

KEY RELATION

$u_x = u \cos(\theta) \quad \text{(Horizontal component)}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

Understanding Key Terms: Scalars & Vectors

In physics, how we describe movement matters. Displacement ( $s$ ) is a vector quantity, telling you the straight-line change in position from start to end, including direction. Velocity ( $v$ ) is also a vector; it's the rate at which displacement changes. Acceleration ( $a$ ), another vector, is the rate at which velocity changes. Always consider the direction for these quantities!

Velocity: $v = \frac{\Delta s}{\Delta t}$ Acceleration: $a = \frac{\Delta v}{\Delta t}$

Speed is the total distance travelled per unit time (a scalar quantity).
Velocity is the rate of change of displacement (a vector quantity). The sign (+ or -) indicates direction.
Acceleration is the rate of change of velocity (a vector quantity).
Example: If 'up' is the positive direction, an object moving upwards at 5 m/s has a velocity of +5 m/s. An object moving downwards at 5 m/s has a velocity of -5 m/s. Both have a speed of 5 m/s.

Not clear?

The SUVAT Equations: Your Toolkit for Motion

When an object moves with uniform (constant) acceleration, we can use a set of four powerful equations to link its motion variables. These are commonly known as the SUVAT equations, named after the quantities they relate: displacement ( $s$ ), initial velocity ( $u$ ), final velocity ( $v$ ), acceleration ( $a$ ), and time ( $t$ ). Mastering these is crucial for exam success.

$v = u + at$ $s = \frac{1}{2}(u+v)t$ $s = ut + \frac{1}{2}at^2$ $v^2 = u^2 + 2as$

Always list your knowns ( $s, u, v, a, t$ ) and what you need to find.
Select the SUVAT equation that includes these variables and excludes the one you don't know or need.
Remember to assign a consistent positive direction; negative values will indicate the opposite direction.
If an object starts from rest or is dropped, its initial velocity ( $u$ ) is $0 \, \text{m/s}$ .

Not clear?

Motion Under Gravity: Special Cases

A common scenario for uniform acceleration is objects moving under gravity. Near Earth's surface, the acceleration due to gravity ( $g$ ) is approximately $9.81 \, \text{m/s}^2$ downwards. This value is constant for objects in free fall (ignoring air resistance) and is crucial in many problems.

EXAM TIP

When dealing with vertical motion, always establish a positive direction (e.g., upwards or downwards) and stick to it! If upwards is positive, then 'g' will be $-9.81 \, \text{m/s}^2$ for an object falling down.

Not clear?

Graphical Analysis of Motion

Graphs provide a powerful visual representation of motion. A displacement-time graph shows an object's position over time, where its gradient reveals the object's velocity. A velocity-time graph illustrates how velocity changes over time; here, the gradient gives the acceleration, and the area under the graph provides the total displacement. Curved lines on a velocity-time graph indicate non-uniform acceleration.

Displacement-time graph: Gradient = velocity.
Velocity-time graph: Gradient = acceleration.
Velocity-time graph: Area under curve = displacement.
A straight line on a velocity-time graph means uniform acceleration.
A horizontal line on a velocity-time graph means constant velocity (zero acceleration).

Not clear?

Motion in Two Dimensions: Projectile Power!

When an object, like a thrown ball, moves in two dimensions (e.g., horizontally and vertically), we call this projectile motion. The key insight here is that the horizontal and vertical components of motion are entirely independent of each other. This means you can apply the SUVAT equations separately to each direction. To do this, you first resolve the initial velocity into its horizontal and vertical components using trigonometry.

$u_x = u \cos(\theta) \quad \text{(Horizontal component)}$ $u_y = u \sin(\theta) \quad \text{(Vertical component)}$

Horizontal motion: Constant velocity (assuming no air resistance), so acceleration $a_x = 0 \, \text{m/s}^2$ .
Vertical motion: Uniform acceleration due to gravity, $a_y = g = 9.81 \, \text{m/s}^2$ downwards.
The time ( $t$ ) is the only variable common to both horizontal and vertical components.

EXAM TIP

For projectile motion, break the initial velocity into horizontal and vertical components using trigonometry. Treat each component as a separate 1D problem, but remember they share the same time of flight!

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A car accelerates uniformly from rest to a speed of $20.0 \, \text{m/s}$ in $5.00 \, \text{s}$ . Calculate the distance it travels during this time.

1
Identify knowns:

EXAMPLE 2

A ball is thrown vertically upwards from the ground with an initial speed of 15.0 m/s. Ignoring air resistance, calculate the maximum height it reaches. (Take g = 9.81 m/s²)

1
Define direction and list knowns: Let's define the upward direction as positive.

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAEquations of motion

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

v–t area: The total displacement of the object.
typical initial velocity: $0 \, \text{m/s}$
Displacement ( $s$ ): The overall change in position from a starting point, including direction (a vector quantity).
s–t gradient: The object's velocity.
Scalar or vector?: Velocity is a vector quantity (it has both magnitude and direction).

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 15 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

Speed is the total distance travelled per unit time (a scalar quantity).
Velocity is the rate of change of displacement (a vector quantity). The sign (+ or -) indicates direction.
Acceleration is the rate of change of velocity (a vector quantity).
Example: If 'up' is the positive direction, an object moving upwards at 5 m/s has a velocity of +5 m/s. An object moving downwards at 5 m/s has a velocity of -5 m/s. Both have a speed of 5 m/s.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/23 · Q2(b)(ii)

PhysicsMay/June 2024

(b) (ii)

Determine the vertical distance travelled by the object.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/23/M/J/24

Question 2 of 29702/22 · Q2(a)(ii)

PhysicsMay/June 2024

(a) (ii)

By drawing a suitable line on Fig. 2.1, determine the acceleration of the skydiver at time t = 9.0 s.

acceleration = .............................................................. ms-2

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/22/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

What is the difference between speed and velocity in physics?

When can I use the SUVAT equations?

How do I deal with negative values for displacement, velocity, or acceleration?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/23 · Q2(b)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS1.4 Scalars and vectors NEXT →3.1 Momentum and Newton's laws of motion

Discuss Equations of motion

Ask, share and discuss with other Physics students

19702 Physics: June 2026 thresholds are out — post your components1 #1How did everyone find the June 2026 Physics A-Level papers?3 #14Why is centripetal force not a real force?2 #2Interesting Diagram0 #

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Revise Equations of motion for Cambridge 9702 (2.1)

Looking for free Physics 9702 notes on Equations of motion? This A-Level lesson covers official syllabus point 2.1 on Paper 1: Multiple Choice / Paper 2: AS Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Equations of motion 9702 revision", "9702 2.1 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

2.1Physics25 min readPREMIUM

Equations of motion

BY THE END, YOU CAN…

exam checklist — tick these off

1Apply SUVAT equations to solve problems involving uniform acceleration.
2Interpret and draw displacement-time and velocity-time graphs, calculating gradient and area.
3Analyse projectile motion by resolving it into independent horizontal and vertical components.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Equations of motion

Cambridge 9702 Paper 2 — Equations of motion (2.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
Speed is the total distance travelled per unit time (a scalar quantity).
2
Velocity is the rate of change of displacement (a vector quantity). The sign (+ or -) indicates direction.
3
Acceleration is the rate of change of velocity (a vector quantity).
4
Example: If 'up' is the positive direction, an object moving upwards at 5 m/s has a velocity of +5 m/s. An object moving downwards at 5 m/s has a velocity of -5 m/s. Both have a speed of 5 m/s.

What this topic covers

The official Cambridge syllabus points this lesson works through.

2.1.1
Define and use distance, displacement, speed, velocity and acceleration
2.1.2
Use graphical methods to represent distance, displacement, speed, velocity and acceleration
2.1.3
Determine displacement from the area under a velocity-time graph
2.1.4
Determine velocity using the gradient of a displacement-time graph
2.1.5
Determine acceleration using the gradient of a velocity-time graph
2.1.6
Derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line
2.1.7
Solve problems using equations that represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance
2.1.8
Describe an experiment to determine the acceleration of free fall using a falling object
2.1.9
Describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Figure Interactive1 / 3

Trajectory Horizontal and vertical motion combine into a parabola; scrub time to fly it.

67 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

67 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

The Physics ClassroomStart here · 19702 2.1 · IB A.1
Kinematic Graphing
A moped leaves a trail of dots; set the initial velocity, acceleration and time and watch the position-, velocity- and acceleration-time graphs
Why this one: Set u, a and t for the moped and watch the dot spacing, the s–t curve and the v–t line grow together: SUVAT on screen.
Try this
1. Set the acceleration to zero and read the three graphs.
2. Add a positive acceleration and compare the dot spacing.
3. Give the initial velocity and acceleration opposite signs.
Look for The gradient of the position-time graph equals the value shown on the velocity-time graph.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN PhysicsStart here · 29702 2.1 · IB A.1
Linear Motion – Graphs of x, v, and a
Set velocity and acceleration for linear motion; read x-t, v-t and a-t graphs
Why this one: Constant a turns the x–t graph into a parabola and the v–t graph into a straight line of gradient a.
Try this
1. Set a velocity with zero acceleration and read the x-t graph.
2. Add a positive acceleration and compare the x-t and v-t graphs.
3. Set a negative acceleration and compare.
Look for Constant velocity gives a straight x-t line; constant acceleration gives a parabola in x-t and a straight v-t line.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 39702 2.1 · IB A.1
1D Kinematics: Velocity vs. Time Graph
Shape a straight-line v-t graph by dragging points; read off displacement, acceleration and motion
Why this one: Drag the v–t line and read displacement as the signed area and acceleration as the gradient.
Try this
1. Drag the points to make a constant positive velocity and read the displacement.
2. Make the line slope down through zero velocity.
3. Make the line steeper and read the acceleration.
Look for Displacement is the signed area under the v-t line and acceleration is its gradient.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
PhETStart here · 49702 2.1
Projectile Motion
Fire a cannon with chosen speed and angle; trace the path with or without air resistance.
Why this one: Switch on velocity vectors: the horizontal arrow never changes while the vertical one grows by g each second.
Try this
1. Set 15 m/s at 45° with air resistance off — note the range, then try 30° and 60°.
2. Fire horizontally from height; use the tape to check s = ½gt² for the drop.
3. Turn on velocity vectors — the horizontal arrow never changes.
Look for Horizontal velocity is constant; vertical motion is uniform acceleration g — equal ranges at complementary angles.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
The Physics ClassroomStart here · 59702 2.1 · IB A.1
Graph That Motion
Match 11 animated motions to their position-time and velocity-time graphs
Why this one: Match a moving object to its s–t and v–t graphs; a curving s–t pairs with a sloping v–t.
Try this
1. Watch a motion and choose its position-time graph.
2. Choose its velocity-time graph.
3. Check and move to the next motion.
Look for A curved position-time graph pairs with a sloping velocity-time graph.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

More simulations62 more on this topic — core ones first

PhETCoreJava · best on a laptop9702 2.1
The Moving Man
Drag the man along the line, or type in position, velocity and acceleration, and watch all three graphs update together.
Try this
1. Drag the man at a steady walk — the velocity graph is flat.
2. Set an acceleration and play — the position graph curves.
3. Walk left then right — note where velocity crosses zero.
Look for Gradient of x–t is v; gradient of v–t is a; turning points of x are where v = 0.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
oPhysicsCore9702 1.4 · 9702 2.1 · IB A.1
Relative Velocity: Boat Crossing a River
Set boat heading, boat speed and river speed; watch the resultant path across the river
Try this
1. Point the boat straight across with the river flowing and watch the path.
2. Angle the heading upstream until the path is straight across.
3. Set the river speed equal to the boat speed and try to cross directly.
Look for The boat’s path follows the vector sum of boat velocity and river velocity, so heading and path differ whenever the river flows.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 2.1 · IB A.1
Uniform Acceleration in One Dimension: Motion Graphs
Adjust initial position, velocity and acceleration; watch the motion and its x-t, v-t, a-t graphs together
Try this
1. Set acceleration to zero and a positive initial velocity; compare the three graphs.
2. Give a positive initial velocity and a negative acceleration.
3. Set initial velocity to zero and vary only the acceleration.
Look for The v-t gradient equals the a-t value and the x-t gradient equals the v-t value, so a straight v-t line pairs with a parabolic x-t curve.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 2.1 · IB A.1
Position, Velocity, and Acceleration vs. Time Graphs
Slide points on a v-t graph; the x-t and a-t graphs update to match the motion
Try this
1. Slide the v-t points to make a horizontal line and look at the x-t graph.
2. Make the v-t line slope upward through zero.
3. Make a v-t segment slope downward and check the sign on the a-t graph.
Look for Where the v-t line crosses zero the x-t graph turns around, and the a-t value is the v-t gradient.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 2.1 · IB A.1
Kinematics Graphs: Adjust the Acceleration
Set initial position/velocity then adjust acceleration; see x-t, v-t and a-t graphs of the object
Try this
1. Set initial velocity positive and acceleration zero, then run.
2. Keep the same initial velocity and set a negative acceleration.
3. Double the acceleration and compare the v-t slopes.
Look for Doubling the acceleration doubles the v-t gradient and makes the x-t parabola curve more tightly.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 2.1 · IB A.1
Uniform Acceleration in One Dimension
Adjust x0, v0 and a for a car under uniform acceleration; run and watch the resulting motion and data
Try this
1. Set v0 positive and a = 0, then run.
2. Set v0 positive and a negative, run, and watch the car reverse.
3. Set v0 = 0 and compare runs at two values of a.
Look for With v0 and a of opposite sign the car slows, stops momentarily and returns; the data follow v = v0 + at.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$v = \frac{\Delta s}{\Delta t}$

Tap a symbol — great for exam definitions

KEY RELATION

= u + at

Tap a symbol — great for exam definitions

KEY RELATION

$u_x = u \cos(\theta) \quad \text{(Horizontal component)}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

Understanding Key Terms: Scalars & Vectors

Velocity: $v = \frac{\Delta s}{\Delta t}$ Acceleration: $a = \frac{\Delta v}{\Delta t}$

Speed is the total distance travelled per unit time (a scalar quantity).
Velocity is the rate of change of displacement (a vector quantity). The sign (+ or -) indicates direction.
Acceleration is the rate of change of velocity (a vector quantity).
Example: If 'up' is the positive direction, an object moving upwards at 5 m/s has a velocity of +5 m/s. An object moving downwards at 5 m/s has a velocity of -5 m/s. Both have a speed of 5 m/s.

Not clear?

The SUVAT Equations: Your Toolkit for Motion

$v = u + at$ $s = \frac{1}{2}(u+v)t$ $s = ut + \frac{1}{2}at^2$ $v^2 = u^2 + 2as$

Always list your knowns ( $s, u, v, a, t$ ) and what you need to find.
Select the SUVAT equation that includes these variables and excludes the one you don't know or need.
Remember to assign a consistent positive direction; negative values will indicate the opposite direction.
If an object starts from rest or is dropped, its initial velocity ( $u$ ) is $0 \, \text{m/s}$ .

Not clear?

Motion Under Gravity: Special Cases

EXAM TIP

Not clear?

Graphical Analysis of Motion

Displacement-time graph: Gradient = velocity.
Velocity-time graph: Gradient = acceleration.
Velocity-time graph: Area under curve = displacement.
A straight line on a velocity-time graph means uniform acceleration.
A horizontal line on a velocity-time graph means constant velocity (zero acceleration).

Not clear?

Motion in Two Dimensions: Projectile Power!

$u_x = u \cos(\theta) \quad \text{(Horizontal component)}$ $u_y = u \sin(\theta) \quad \text{(Vertical component)}$

Horizontal motion: Constant velocity (assuming no air resistance), so acceleration $a_x = 0 \, \text{m/s}^2$ .
Vertical motion: Uniform acceleration due to gravity, $a_y = g = 9.81 \, \text{m/s}^2$ downwards.
The time ( $t$ ) is the only variable common to both horizontal and vertical components.

EXAM TIP

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A car accelerates uniformly from rest to a speed of $20.0 \, \text{m/s}$ in $5.00 \, \text{s}$ . Calculate the distance it travels during this time.

1
Identify knowns:

EXAMPLE 2

A ball is thrown vertically upwards from the ground with an initial speed of 15.0 m/s. Ignoring air resistance, calculate the maximum height it reaches. (Take g = 9.81 m/s²)

1
Define direction and list knowns: Let's define the upward direction as positive.

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAEquations of motion

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

v–t area: The total displacement of the object.
typical initial velocity: $0 \, \text{m/s}$
Displacement ( $s$ ): The overall change in position from a starting point, including direction (a vector quantity).
s–t gradient: The object's velocity.
Scalar or vector?: Velocity is a vector quantity (it has both magnitude and direction).

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 15 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

Speed is the total distance travelled per unit time (a scalar quantity).
Velocity is the rate of change of displacement (a vector quantity). The sign (+ or -) indicates direction.
Acceleration is the rate of change of velocity (a vector quantity).
Example: If 'up' is the positive direction, an object moving upwards at 5 m/s has a velocity of +5 m/s. An object moving downwards at 5 m/s has a velocity of -5 m/s. Both have a speed of 5 m/s.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/23 · Q2(b)(ii)

PhysicsMay/June 2024

(b) (ii)

Determine the vertical distance travelled by the object.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/23/M/J/24

Question 2 of 29702/22 · Q2(a)(ii)

PhysicsMay/June 2024

(a) (ii)

By drawing a suitable line on Fig. 2.1, determine the acceleration of the skydiver at time t = 9.0 s.

acceleration = .............................................................. ms-2

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/22/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

What is the difference between speed and velocity in physics?

When can I use the SUVAT equations?

How do I deal with negative values for displacement, velocity, or acceleration?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/23 · Q2(b)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS1.4 Scalars and vectors NEXT →3.1 Momentum and Newton's laws of motion

Discuss Equations of motion

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Revise Equations of motion for Cambridge 9702 (2.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Kinematic Graphing

Linear Motion – Graphs of x, v, and a

1D Kinematics: Velocity vs. Time Graph

Projectile Motion

Graph That Motion

The Moving Man

Relative Velocity: Boat Crossing a River

Uniform Acceleration in One Dimension: Motion Graphs

Position, Velocity, and Acceleration vs. Time Graphs

Kinematics Graphs: Adjust the Acceleration

Uniform Acceleration in One Dimension

Key formulas

Full topic notes

Understanding Key Terms: Scalars & Vectors

The SUVAT Equations: Your Toolkit for Motion

Motion Under Gravity: Special Cases

Graphical Analysis of Motion

Motion in Two Dimensions: Projectile Power!

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Equations of motion

Revise Equations of motion for Cambridge 9702 (2.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Kinematic Graphing

Linear Motion – Graphs of x, v, and a

1D Kinematics: Velocity vs. Time Graph

Projectile Motion

Graph That Motion

The Moving Man

Relative Velocity: Boat Crossing a River

Uniform Acceleration in One Dimension: Motion Graphs

Position, Velocity, and Acceleration vs. Time Graphs

Kinematics Graphs: Adjust the Acceleration

Uniform Acceleration in One Dimension

Key formulas

Full topic notes

Understanding Key Terms: Scalars & Vectors

The SUVAT Equations: Your Toolkit for Motion

Motion Under Gravity: Special Cases

Graphical Analysis of Motion

Motion in Two Dimensions: Projectile Power!

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Equations of motion