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Overview

(Unit Two→Linear Motion — Second Secondary, Term 1) 🌳 Concept tree Chapter 3: Force and Motion

├── What you will learn

├── Introduction

├── 1.1 What is force?

├── 1.2 Resultant force

├── 2.1 Observation and the old belief

├── 2.2 Statement of the law

├── 2.3 Consequences of the first law

├── 2.4 Inertia

├── Lesson 3→Momentum

├── 4.1 Statement

├── 4.2 Another statement of the law

├── 4.3 Definition of the newton

├── 4.4 Thinking exercise

├── 4.6 Life applications of the second law (force, time and change of momentum)
├── 4.7 The first law as a special case of the second

├── 5.1 Observations

├── 5.2 Statement

├── 5.3 Properties of action and reaction

├── 5.4 Applications

├── Short answers to typical discussion questions

├── Summary

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What you will learn

The concept of force and how it is measured.
Newton’s first law and the phenomenon of inertia.
Momentum.
Newton’s second law (F = ma; force as the rate of change of momentum); the newton.
Explaining everyday phenomena (collisions, airbags, falling on different surfaces).
Newton’s third law (action and reaction) and its applications.

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Introduction

In the previous chapter we described motion by speed, velocity and acceleration, without asking why things move.
In this chapter we ask what produces acceleration.
The answer is force.
Newton’s three laws of motion, which we study here, are among the most important laws in physics.

Before the seventeenth century no organised theory of motion existed, although many ancient philosophers had tried to explain it.
The greatest credit for founding it goes to two scientists Galileo and Newton.

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1.1 What is force?

"Force" is a word we use every dayyour muscles pull a bag, a car engine starts the car moving, a brake stops it.

Forceis an external influence acting on an object that changes, or tries to change, its state of motion (its velocity in magnitude or direction).

Force is a vector quantity (it has magnitude and direction).
It is measured by a spring balance (spring scale).
Its SI unit is the newton (N).
"Tries to change" if you push a heavy wall and it does not move, your push is still a force, but another force (the reaction of the floor/friction) balances it.

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1.2 Resultant force

Often several forces act on one body.
Their vector sum is the resultant (net) force, written ΣF (read "sigma F").
Forces in the same line are added with signs (+ in one direction, − in the opposite one).
Example 1. A box on the floor is pulled to the right by 30 N and to the left by 10 N (friction). ΣF = 30 − 10 = 20 N to the right.
Example 2. The same box is pulled by 30 N to the right and 30 N to the left. ΣF = 0: the forces are balanced and the box keeps its state of motion.

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2.1 Observation and the old belief

Imagine returning home after a long trip everything is as you left it.
This simple fact, "things stay as they are unless something changes them", is the basis of Newton’s first law.

Everyday experience seems to contradict it if you push a box on the floor, it slides some distance, slows down and stops.
Ancient thinkers concluded that rest is the natural state of matter and that every motion dies away.
Experiments showed that this is wrong the box stops because of friction, a force opposing its sliding.
If friction did not exist (as on very smooth ice, or in space) the box would go on moving for ever without stopping.

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2.2 Statement of the law

Newton’s first law of motion An object remains at rest, or moves with constant velocity in a straight line, unless a resultant force acts on it and changes this state.
Mathematical form ΣF = 0 (the object keeps its state)
where ΣF is the resultant of all forces acting on it.
Several forces may act, but if they cancel each other the resultant is zero.

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2.3 Consequences of the first law

Comparison aspect	Main idea	Keywords
If ΣF = 0, then a = 0	the velocity does not change whether the object is at rest or moving	velocitydoeschangewhether
•	A force is needed to start a stationary object moving or to stop a moving one (that is to change its velocity)	forceneededstartstationary
No force is needed to keep an object moving at constant velocity	(only to cancel friction/air resistance). A car moving steadily on a straight road has an engine force that exactly balances the resistances: ΣF = 0	cancelfrictionresistancesteadily
Example 1.	A car moves at a steady 25 m/s along a straight road. The engine force is 900 N forward. What is the resistance to motion? Since the velocity is constant ΣF = 0 so the resistance is 900 N backward	movessteadyalongstraight

Example 2.→A book rests on a table: its weight (downward) is balanced by the table’s upward force; ΣF = 0, so it remains at rest.

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2.4 Inertia

Newton’s first law is also called the law of inertia.
Inertia is the tendency of a stationary object to remain at rest, and of a moving object to continue moving with the same velocity in a straight line; that is, objects resist any change in their state of rest or motion.
Everyday examples of inertia

A passenger standing in a bus is thrown forward when the bus brakes suddenly: his body tends to keep moving forward.
When a train suddenly moves forward, a small bag lying under a seat appears to slide backward relative to the train, because it tends to stay at rest while the train moves forward under it.
A card under a coin on a glass flick the card away quickly and the coin drops into the glass, since it tends to remain at rest.
Measure of inertia. Observation shows that the difficulty of stopping a moving body depends on its mass and its velocity:

A large truck is hard to stop, a small bicycle is easy, if they move at the same velocity.
A car moving fast is hard to stop; the same car moving slowly is easy to stop.
The two factors together define a new quantity, the momentum.

Chapter 3: Force and Motion · 9 / 23

Lesson 3: Momentum

Momentum (p) is the product of the mass of a body and its velocity:
p = m v

Comparison aspect	Main idea	Keywords
•	It is a vector (same direction as the velocity)	vectorsamedirectionvelocity
Unit	kg·m/s
Dimensional formula	MLT⁻¹
•	A body with larger momentum needs a larger force or a longer time to be stopped	bodylargermomentumneeds
Example 1.	A truck of mass 8000 kg moves at 15 m/s: p = 8000 × 15 = 1.2 × 10⁵ kg·m/s. A cyclist and cycle of total mass 90 kg at 6 m/s: p = 540 kg·m/s. The truck’s momentum is more than 200 times larger	truckmass8000moves
Example 2.	A 0.15 kg ball moves at 20 m/s to the right: p = +3 kg·m/s. After it rebounds at 20 m/s to the left p = −3 kg·m/s the change of momentum is −3 − (+3) = −6 kg·m/s	ballmovesrightAfter
Example 3.	What speed gives a 1200 kg car the same momentum as the truck in Example 1? v = p/m = 1.2 × 10⁵/1200 = 100 m/s (360 km/h)	Whatspeedgives1200

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4.1 Statement

By the first law, an object with no resultant force has no acceleration.
So if a resultant force acts (ΣF ≠ 0) the velocity changes and the object accelerates (a ≠ 0).
Newton’s second law gives the exact relation.
Newton’s second law The resultant force acting on an object is equal to the time rate of change of its momentum.

ΣF = Δp/Δt = (m vf − m vi)/Δt

If the mass is constant:

ΣF = m (vf − vi)/Δt = m Δv/Δt

and since Δv/Δt is the acceleration,

ΣF = m a→or a = ΣF / m

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4.2 Another statement of the law

When a resultant force acts on an object it gives the object an acceleration that is directly proportional to the force and inversely proportional to its mass, and in the direction of the force.

Same mass, greater force → greater acceleration.
Same force, greater mass → smaller acceleration.
Graph of acceleration against force.

For a given mass the graph a–F is a straight line through the origin whose slope is 1/m.
For a smaller mass the slope (and so the acceleration for the same force) is larger.
For example a 100 kg body has twice the acceleration of a 200 kg body under the same force.

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4.3 Definition of the newton

From F = ma→1 newton is the force that gives a mass of 1 kg an acceleration of 1 m/s².

1 N = 1 kg·m/s²

The dimensional formula of force is MLT⁻².
In the CGS system the unit of force is the dyne, and 1 N = 10⁵ dyn.

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4.4 Thinking exercise

A force F on a wooden cube gives it a certain acceleration.
The same force on another cube gives it three times the acceleration.
Since a = F/m with F constant, a ∝ 1/m, so the second cube has one-third of the mass of the first.
Example 1 — F = ma. A car of mass 1200 kg accelerates uniformly at 2.5 m/s². The resultant force = 1200 × 2.5 = 3000 N.
Example 2 — mass. A resultant force of 45 N gives a body an acceleration of 1.5 m/s². m = F/a = 45/1.5 = 30 kg.
Example 3 — net force with friction. A 50 kg crate is pushed by a 200 N force while friction opposes the motion with 120 N. ΣF = 200 − 120 = 80 N; a = 80/50 = 1.6 m/s².

Comparison aspect	Main idea	Keywords
Example 4 — from the change of momentum.	A force acts on a 2 kg body changing its velocity from 3 m/s to 15 m/s in 4 s. Δp = 2 × (15 − 3) = 24 kg·m/s F = 24/4 = 6 N. (Check: a = 12/4 = 3 m/s² F = 2 × 3 = 6 N.)	forceactsbodychanging
Example 5 — velocity after a time.	A 5 kg trolley at rest is pulled by a net force of 10 N for 6 s. a = 10/5 = 2 m/s² v = at = 2 × 6 = 12 m/s	trolleyrestpulledforce

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4.6 Life applications of the second law (force, time and change of momentum)

From F = Δ(mv)/Δt, i.e.
F·Δt = Δ(mv) (the product Ft is called the impulse), the force needed to bring a given moving body to rest depends on the time it takes:

If the change of momentum happens over a longer time, the force is smaller (the effect of the impact is less).
If it happens in a shorter time, the force is larger.
This explains:

A car hitting a wall is more destructive than a car hitting a heap of straw: the wall stops it in a very short time (large force); straw takes longer (smaller force).
A person falling from a height into water is not hurt but falling onto ground may hurt: water brings him to rest more slowly.
The severity of the injury increases with the height of the fall, because the velocity (and so the momentum) at impact increases.
An egg does not break when it falls on a cushion, but it breaks on the floor.
A collision of a large truck with a wall is more destructive than that of a small truck: larger mass → larger momentum → larger force for the same stopping time.
in cars increase the time over which the driver’s body comes to rest in a collision, reducing the force on him.
Similarly, a cricket or football goalkeeper pulls the hands back while catching a fast ball to lengthen the stopping time.

✍️ Worked examples

Example 6 (numerical). A 0.15 kg ball moving at 20 m/s is caught and stopped.
Stopped in 0.01 s (hard hands): F = 0.15 × 20/0.01 = 300 N.
Stopped in 0.10 s (hands drawn back): F = 0.15 × 20/0.10 = 30 N, ten times smaller.
Example 7 (airbag). A driver of mass 70 kg moving at 14 m/s is stopped in 0.05 s by a rigid steering wheel: F = 70 × 14/0.05 = 19 600 N. With an airbag extending the time to 0.25 s: F = 70 × 14/0.25 = 3 920 N.

Chapter 3: Force and Motion · 15 / 23

4.7 The first law as a special case of the second

If ΣF = 0 then, from ΣF = ma, a = 0 and the velocity is constant.
So the first law follows from the second law as a special case (zero resultant force).

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5.1 Observations

A balloon blown up and released flies off as the air rushes out.
A person on a rolling chair who pushes a wall with his feet moves away from the wall.
A rifle "kicks back" when a bullet is fired.
All these cases are explained by Newton’s third law.

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5.2 Statement

Comparison aspect	Main idea	Keywords
Newton’s third law	When one object exerts a force on a second object the second exerts a force on the first that is equal in magnitude and opposite in direction. In short: for every action there is an equal and opposite reaction	objectexertsforcesecond
Mathematical form	F₁ = − F₂

Forces occur in pairs.
Example two spring balances hooked together and pulled give identical readings: the force of the first on the second equals that of the second on the first.

Chapter 3: Force and Motion · 18 / 23

5.3 Properties of action and reaction

Comparison aspect	Main idea	Keywords
There is no single force	in the universe action and reaction appear together and disappear together	universeactionreactionappear
•	They are equal in magnitude opposite in direction and have the same line of action	equalmagnitudeoppositedirection
They have the same nature	if the action is a gravitational force so is the reaction	actiongravitationalforcereaction
They do not cancel each other	because they act on two different bodies. (Forces cancel only if they act on the same body.)	becausedifferentbodiesForces

Thinking corner→when a large truck collides with a small car, which receives the larger force? Both receive forces of equal magnitude. The car is damaged more, and gains a larger acceleration (a = F/m), because its mass is smaller.

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5.4 Applications

Comparison aspect	Main idea	Keywords
Rocket propulsion	burning gas of large mass is expelled backwards (downwards) at high speed the reaction on the rocket is a thrust forward (upwards). A rocket needs no air to push against so it works in space	burninglargemassexpelled
Recoil of a gun	the gun pushes the bullet forward the bullet pushes the gun backward with an equal force but the gun’s much larger mass gives it a very small acceleration	pushesbulletforwardbackward
Swimming/walking	a swimmer pushes the water back the water pushes him forward when walking your foot pushes the ground backward and the ground pushes you forward	swimmerpusheswaterback
Space	an astronaut who throws an object in one direction moves in the opposite direction. This suggests how a spacecraft can change its direction outside the atmosphere: by ejecting gas in the direction opposite to the desired change	astronautthrowsobjectdirection

✍️ Worked examples

Example 1.
Two skaters stand on smooth ice.
Skater A (60 kg) pushes skater B (40 kg) with a force of 120 N.
Then B pushes A with 120 N in the opposite direction (third law).
a_B = 120/40 = 3 m/s²; a_A = 120/60 = 2 m/s², in opposite directions.
The lighter skater accelerates more, although the forces are equal.
Example 2.
A hammer hits a nail with 400 N.
The nail pushes back on the hammer with 400 N in the opposite direction.
The nail moves in because it has little resistance; the hammer slows down because of the force of the nail.
Example 3. A 0.02 kg bullet leaves a 4 kg rifle with an acceleration of 5000 m/s² during the shot. Force on the bullet = 0.02 × 5000 = 100 N. Force on the rifle = 100 N backward; its acceleration = 100/4 = 25 m/s² backward (so a firm grip is needed).
Example 4.
Which statement is wrong?
"The weight of a book and the upward force of the table on it are an action-reaction pair." They act on the same object (the book) and are balanced, so they are not an action–reaction pair; the third-law pair of the table’s force on the book is the force of the book on the table.

Chapter 3: Force and Motion · 20 / 23

Short answers to typical discussion questions

Comparison aspect	Main idea	Keywords
•	A train suddenly moves forward where does a small bag under a seat go? Relative to the train it moves backward because of its inertia (it tends to stay at rest)	trainsuddenlymovesforward
Why is the first law a special case of the second?	When ΣF = 0 ma = 0 so a = 0 — constant velocity	constantvelocity
What happens when an astronaut throws an object?	He moves in the opposite direction (third law) a spacecraft can change direction by expelling gas	movesoppositedirectionthird

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Summary

Comparison aspect	Main idea	Keywords
Force	an external influence that changes or tries to change the state of motion unit newton (N) measured by a spring balance	externalinfluencechangestries
First law	ΣF = 0 → rest or constant velocity inertia is the resistance to change of the state of motion	restconstantvelocityinertia
•	Momentum p = mv (kg·m/s)	Momentum
Second law	ΣF = Δp/Δt = ma a ∝ F a ∝ 1/m 1 N = 1 kg·m/s². A longer time of impact gives a smaller force	longertimeimpactgives
Third law	F₁ = −F₂ equal opposite same nature on different bodies appear and disappear together	equaloppositesamenature
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Test yourself on this lesson

The lesson’s question bank is split across the points above; each point has its own questions underneath.
To work through the whole bank on one page:

Chapter 3: Force and Motion · 22 / 23

Part 23

📖

📌 Comprehensive Scientific Terminology & Definitions:

Comparison aspect	Main idea	Keywords
Linear Momentum (p)	The product of an object’s mass and its velocity: p = m v (vector quantity sharing the direction of velocity measured in kg·m/s or N·s)	productobjectmassvelocity
Newton’s 1st Law (Inertia)	An object continues in its state of rest or uniform motion in a straight line unless acted upon by a net external resultant force: ΣF = 0	objectcontinuesstaterest
Newton’s 2nd Law	The net external force acting on a body is equal to the time rate of change of its linear momentum: F_net = Δp / Δt = m a. The Newton is defined as the force that accelerates a 1-kg mass at 1 m/s².	externalforceactingbody
Newton’s 3rd Law	For every action, there is an equal and opposite reaction: F_AB = -F_BA. Action and reaction forces act on different bodies simultaneously and never cancel each other.	everyactionequalopposite
Newton’s Law of Universal Gravitation	Every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers: F = G (m₁ m₂) / r²	Everyparticleuniverseattracts

⚖️ Governing Scientific Laws, Principles & Mathematical Formulas:

Comparison aspect	Main idea	Keywords
Momentum	p = m v (kg·m/s)
Newton’s 2nd Law	F = m a = Δp / Δt
Weight	W = m g (Mass m is constant Weight W varies with g)	Massconstantvaries
Universal Gravitation	F = G (m₁ m₂) / r² (G = 6.67 × 10⁻¹¹ N·m²/kg²)
Gravitational Field Strength	g = G M / r²

🔍 In-Depth Explanations, Deductions & Core Concepts:

Comparison aspect	Main idea	Keywords
Why do action and reaction forces not produce equilibrium?	Because they act on two different bodies whereas equilibrium requires opposing forces to act on the exact same single body	Becausedifferentbodieswhereas
Why do airbags reduce collision injuries?	Airbags prolong the collision contact time (Δt). Since impact force F = Δp / Δt lengthening the impact duration greatly minimizes the force experienced by the passenger	prolongcontacttimeSince
Why do passengers lurch forward when a bus suddenly brakes?	Due to inertia: the passengers’ bodies tend to maintain their forward state of motion	inertiabodiestendmaintain

Property	Mass (m)	Weight (W)
Definition	Measure of inertia and amount of matter in a body	Gravitational pull exerted on a body by Earth
Quantity Type	Fundamental Scalar	Derived Vector (directed toward center of Earth)
SI Unit	Kilogram (kg)	Newton (N)
Variation with Location	Constant everywhere in the universe	Varies with local gravitational acceleration (W = mg)

💡 High-Yield Exam Traps & Key Takeaways:

1 Newton = 1 kg·m/s² = 1 J/m.
Apparent weight in an elevator accelerating upward: N = m(g + a) (feels heavier); accelerating downward: N = m(g – a) (feels lighter).

Chapter 3: Force and Motion · 23 / 23

Curriculum

Physics — Second Secondary

Physics — Second Secondary

Physics — Second Secondary 2026/2027

Chapter 3: Force and Motion

├── What you will learn

├── Introduction

├── 1.2 Resultant force

├── 2.1 Observation and the old belief

├── 2.2 Statement of the law

├── 2.3 Consequences of the first law

├── 2.4 Inertia

├── 4.1 Statement

├── 4.2 Another statement of the law

├── 4.3 Definition of the newton

├── 4.4 Thinking exercise

├── 5.1 Observations

├── 5.2 Statement

├── 5.3 Properties of action and reaction

├── 5.4 Applications

├── Summary

ΣF = Δp/Δt = (m vf − m vi)/Δt

ΣF = m (vf − vi)/Δt = m Δv/Δt

and since Δv/Δt is the acceleration,

1 N = 1 kg·m/s2

✍️ Worked examples

✍️ Worked examples

Test yourself on this lesson

📌 Comprehensive Scientific Terminology & Definitions:

⚖️ Governing Scientific Laws, Principles & Mathematical Formulas:

🔍 In-Depth Explanations, Deductions & Core Concepts:

💡 High-Yield Exam Traps & Key Takeaways:

Well done! You finished this lesson

1 N = 1 kg·m/s²