• 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.
• The meaning of motion, and its types (translational and periodic).
• Speed and velocity; uniform and variable velocity; instantaneous and average velocity.
• Drawing and reading the displacement–time graph.
• Acceleration and its types (positive, zero, negative); drawing and reading the velocity–time graph.
• Analysing motion diagrams and graphs of motion in a straight line.

🌳 Concept tree

1. Speed, Uniform Acceleration and Laws of Motion
2. ├── Why study motion?

├── Definition of motion

├── Types of motion

├── Why we need velocity

├── Speed and velocity

├── Converting units

├── Worked examples

├── Uniform and non-uniform (variable) velocity

├── Instantaneous and average velocity

├── Worked examples

├── How to draw it

├── Reading the displacement–time graph

├── Worked examples

├── Definition

├── Types of acceleration

├── Worked examples

├── Reading the graph

├── Analysing a multi-stage graph

├── Extension — displacement from the v–t graph

├── Motion (dot) diagrams

├── More worked examples

• ├── Short answers to typical discussion questions

├── Summary

├── Introduction

• ├── What is force?

├── Resultant force

├── Observation and the old belief

├── Statement of the law

├── Consequences of the first law

├── Inertia

├── Momentum

├── Statement

├── Another statement of the law

├── Definition of the newton

├── Thinking exercise

├── Worked examples

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

├── Observations

├── Statement

├── Properties of action and reaction

├── Applications

├── Worked examples

• ├── Short answers to typical discussion questions

└── Summary

• We often say "fast" or "slow", but these words are not scientific.
• To describe motion exactly we need a quantity — velocity (and speed).
• Velocity

• is the displacement covered by the object in one second, or the rate of change of displacement with time.
• Its units m/s (SI) or km/h.

velocity v = displacement ÷ time = Δd / Δt

• Here Δd (the change in position) is the displacement and Δt is the time taken.

• Imagine a runner photographed at equal time intervals (for example every second).

• slope = Δ(displacement) / Δ(time) = velocity

• Take the direction of the velocity as the positive direction.
• A small ball rolling on a smooth surface with different slopes shows all three cases:

• If velocity and acceleration have the same direction (same sign), the object speeds up — even if both are negative.
• If they have opposite directions (opposite signs), the object slows down.
• If acceleration = 0, the velocity is constant. It is not necessarily zero (e.g. a car at a steady 20 m/s has zero acceleration).
• Life application.

• Inside every car there are three controls that change the velocity: the accelerator (gas) pedal increases the magnitude, the brake pedal decreases it, and the steering wheel changes its direction.
• Each of them produces an acceleration.

• (Not stated in the book text, but needed for graph questions like "find the total distance covered".)
  The area between the v–t graph and the time axis equals the displacement (distance for motion in one direction).
• For the graph above:

1. v = u + at (this is just the definition of acceleration
2. a = (v − u)/t),

s = ½(u + v)t (area of a trapezoid),

• s = ut + ½at², v² = u² + 2as.
• Example. A car starts from rest and accelerates at 2 m/s² for 10 s. Then v = 0 + 2 × 10 = 20 m/s and the distance s = ½ × 2 × 10² = 100 m (check: area of the triangle ½ × 10 × 20 = 100 m).

• Motion = change of position with time relative to another object; types: translational and periodic.
• Velocity v = Δd/Δt (vector, m/s); speed is the scalar magnitude. 1 km/h = 5/18 m/s.
• Uniform velocity equal displacements in equal times; variable velocity: unequal.
• Instantaneous velocity = slope of tangent on d–t; average velocity = total displacement/total time = slope of chord.
• Acceleration a = Δv/Δt (m/s², LT⁻²); positive, zero or negative; same signs → speeding up; opposite signs → slowing down.
• d–t graph slope = velocity; v–t graph slope = acceleration (area = displacement).

• 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.

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

• 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.

• 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.

✍️ 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.

• 📖

🔍 In-Depth Explanations, Deductions & Multi-Book Insights:

General & Integrated Science (2026/2027)

• Lesson 1 – Speed, Uniform Acceleration and Laws of Motion
• Kinematics describes the motion of physical bodies without regarding the forces causing it.
• We derive the concepts of regular and irregular velocity, acceleration (a = Δv / Δt), graphical representations of motion, and Newton's laws governing mechanical motion in science.

🌳 Conceptual Hierarchy Tree

Kinematics and Dynamics Foundations