Chapter Two: Motion
Rest and Motion · Types of Motion · Scalar & Vector Quantities · Distance vs Displacement · Speed vs Velocity · Acceleration · Equations of Motion · Laws of Falling Bodies · Graphs · Board Questions 2016–2025 — All in One Complete Guide.
📋 Chapter 2 — Complete Content Structure
2.1 Rest and Motion
Understanding the fundamental concepts of position, rest, motion, and the relative nature of these states is the foundation of kinematics. This section covers reference points, positional descriptions, and the crucial idea that all motion is relative.
🔍 2.1.1 Position & Reference Point
Meaning of Position: The position of an object describes where it is located at a particular time. To specify a position completely, we need a reference point (origin) and a set of coordinates or a direction and distance from that reference point.
Reference Point / Origin: A fixed point from which we measure the position of an object. Without a reference point, describing the location of any object becomes meaningless.
Specifying Position: Position requires both distance and direction from the reference point. For example, "The book is 3 meters to the right of the door" specifies both magnitude and direction.
🪑 2.1.2 Rest
Definition: An object is said to be at rest when its position does not change with respect to a reference point as time passes.
Example: A book lying on a table is at rest with respect to the table, as its position relative to the table remains unchanged over time.
🏃 2.1.3 Motion
Definition: An object is said to be in motion when its position changes with time with respect to a reference point.
Example: A car moving along a road changes its position with respect to a tree on the roadside, so it is in motion.
🔄 2.1.4 Relative Nature of Rest and Motion
Key Concept: Rest and motion are relative. The same object may be at rest relative to one observer and in motion relative to another.
NCTB Example: A passenger sitting inside a moving train. The passenger is at rest relative to the train seat and other passengers, but is in motion relative to an observer standing at the station platform.
Thus, when we describe something as "stationary" or "moving," we must always specify the reference frame.
⭐ Exam Focus — Very Important
- Reference point
- Rest
- Motion
- Relative rest
- Relative motion
2.2 Different Types of Motion
Motion can be classified into several categories based on the path followed, the nature of the movement, and the relationship between different parts of the object. NCTB discusses multiple forms of motion essential for Class 9-10 students.
📏 2.2.1 Linear Motion
Definition: Motion along a straight line is called linear motion.
Examples:
- A car moving on a straight road
- A stone falling vertically downward
- A bullet moving along a straight path
⭕ 2.2.2 Circular Motion
Definition: Motion in which an object moves around a fixed point/axis while maintaining a fixed distance from it is called circular motion.
Examples:
- Hands of a clock
- Blades of a fan
- Moon revolving around Earth
🚗 2.2.3 Translational Motion
Definition: When all particles of an object move through the same distance in the same direction during the same time interval, the motion is called translational motion.
Example: A car moving forward on a straight road — every part of the car (doors, wheels' centers, body) moves the same distance in the same direction.
⏰ 2.2.4 Periodic Motion
Definition: Motion that repeats itself at regular intervals of time is called periodic motion.
Examples:
- Motion of a pendulum
- Revolution of Earth around the Sun
- Motion of clock hands
- Vibrating objects
🔁 2.2.5 Oscillatory Motion
Definition: To-and-fro motion about a mean/equilibrium position is called oscillatory motion.
Examples:
- Simple pendulum
- Child on a swing
- Mass attached to a spring
🎯 2.2.6 Simple Harmonic Motion (SHM)
Definition: A special type of periodic/oscillatory motion in which the restoring tendency is related to displacement from the mean position.
For Class 9–10, focus on: mean position, to-and-fro motion, maximum displacement, and periodic nature.
Key Relationship: Every SHM is periodic motion, but not every periodic motion is SHM. SHM requires a restoring force proportional to displacement.
2.3 Scalar and Vector Quantities
Physical quantities are categorized into two fundamental types: scalars (magnitude only) and vectors (magnitude + direction). This distinction is critical for understanding distance vs displacement and speed vs velocity.
📊 Scalar Quantity
A physical quantity that can be completely expressed by magnitude only.
Examples: Distance, Speed, Mass, Time, Temperature, Length
📈 Vector Quantity
A physical quantity that requires both magnitude + direction.
Examples: Displacement, Velocity, Force, Acceleration, Position
| Scalar | Vector |
|---|---|
| Distance | Displacement |
| Speed | Velocity |
| Mass | Force |
| Time | Acceleration |
| Temperature | Position |
| Length | Momentum |
2.4 Distance and Displacement
Distance and displacement are two different ways to describe how far an object has travelled. Understanding their differences is one of the most common board exam questions.
📏 Distance
The total length of the actual path travelled by an object.
Nature: Scalar | SI unit: metre (m) | Dimension: [L]
Distance is always positive and depends on the actual path taken. It can never be negative or zero when motion has occurred.
🧭 Displacement
The shortest straight-line distance from initial to final position with direction.
Nature: Vector | SI unit: metre (m) | Dimension: [L]
Displacement depends only on initial and final positions. It can be positive, negative, or zero depending on chosen direction.
⭐ Special Case — Circular Track
If a person travels around a circular track and returns to the starting point:
Displacement = 0 (since initial and final positions are the same)
Distance ≠ 0 (since the actual path length travelled is the circumference)
| Distance | Displacement |
|---|---|
| Scalar | Vector |
| Actual path | Shortest directed path |
| Cannot be negative | Can be positive, negative, or zero |
| Depends on path | Depends on initial and final positions |
| Always ≥ magnitude of displacement | Magnitude ≤ distance |
2.5 Speed and Velocity
Speed and velocity describe how fast an object is moving, but they differ in their treatment of direction. Speed is scalar, while velocity is a vector quantity.
⚡ 2.5.1 Speed
Rate of change of distance with time.
SI unit: m·s⁻¹ | Dimension: [LT⁻¹]
📊 2.5.2 Average Speed
🎯 2.5.3 Velocity
Rate of change of displacement with time. Velocity is a vector quantity.
SI unit: m·s⁻¹ | Dimension: [LT⁻¹]
📈 2.5.4 Average Velocity
Important: For straight-line motion in one direction, speed = |velocity|. But generally, average speed ≠ average velocity, especially when direction changes.
2.6 Acceleration and Retardation
Acceleration measures how quickly velocity changes. It is a vector quantity that can be positive (speeding up) or negative (slowing down / retardation).
🔬 Definition & Formula
Acceleration is the rate of change of velocity with time.
Where: u = initial velocity, v = final velocity, t = time, a = acceleration
SI Unit: m/s² | Dimension: [LT⁻²]
✅ Uniform Acceleration
Velocity changes by equal amounts in equal intervals of time.
Example: 5, 10, 15, 20, 25 m/s — velocity increases by 5 m/s every second.
⚠️ Non-uniform Acceleration
Velocity does not change by equal amounts in equal intervals of time.
Example: 2, 5, 11, 20, 35 m/s — velocity changes irregularly.
🚫 Retardation / Deceleration
When velocity decreases with time, acceleration acts opposite to the direction of motion, so a < 0.
Example: A car slows from 20 m/s to 10 m/s in 5 s:
Therefore, retardation = 2 m/s²
2.7 Equations of Motion
The three equations of motion for uniformly accelerated motion are fundamental to solving kinematics problems. They connect initial velocity (u), final velocity (v), acceleration (a), time (t), and displacement (s).
📋 Equations of Motion — Formula Sheet
2. s = ut + ½at²
3. v² = u² + 2as
4. s = [(u + v) / 2] × t
5. Sₜₕ = u + a(2t - 1)/2 (distance in tᵗʰ second)
Symbols: u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement
Unit Conversion: 1 km/h = 5/18 m/s | 60 km/h = 16.67 m/s
🔑 Variable Selection Guide
| Formula | Variables Present | Variable Absent |
|---|---|---|
| v = u + at | u, v, a, t | s |
| s = [(u+v)/2]t | s, u, v, t | a |
| s = ut + ½at² | s, u, a, t | v |
| v² = u² + 2as | s, u, v, a | t |
2.8 Laws of Falling Bodies
Free fall under Earth's gravity is a special case of uniformly accelerated motion with acceleration g ≈ 9.8 m/s². Galileo formulated three fundamental laws governing falling bodies.
🌍 Acceleration Due to Gravity (g)
When an object falls freely under Earth's gravitational influence, it experiences acceleration due to gravity:
For a body falling from rest (u = 0):
h = ½gt²
v² = 2gh
🥇 Galileo's First Law
Bodies falling freely from rest from the same height, in the absence of air resistance, cover equal distances in equal times.
Key Insight: Mass does not determine the acceleration of a freely falling body.
🥈 Galileo's Second Law
The velocity acquired by a freely falling body from rest is directly proportional to time.
🥉 Galileo's Third Law
Distance travelled by a freely falling body from rest is proportional to the square of time.
⭐ Feather vs Stone — Critical Concept
In normal air: A stone reaches the ground before a feather because of air resistance.
In a vacuum: Both fall with the same acceleration g and reach the ground simultaneously if released from the same height at the same time.
🪂 Falling Body Equations — Complete Set
v = u + gt
h = ut + ½gt²
v² = u² + 2gh
From rest (u = 0):
v = gt
h = ½gt²
v² = 2gh
Thrown upward:
v = u - gt
h = ut - ½gt²
v² = u² - 2gh
H_max = u² / 2g | T_up = u / g | T_total = 2u / g
Interactive MCQ Bank — Chapter 2 Motion
Test your understanding with these 25 interactive multiple-choice questions. Click on any option to see instant feedback.
Board Questions & Important Patterns (2016–2025)
Based on available board archives, Motion is one of the most calculation-heavy chapters. Below is a summary of the most repeated board patterns and important questions from 2016 to 2025.
🏆 Most Repeated Board Patterns
| Topic | Importance Level |
|---|---|
| Rest & motion / reference point | ⭐⭐⭐⭐ |
| Types of motion | ⭐⭐⭐⭐ |
| Scalar & vector | ⭐⭐⭐⭐⭐ |
| Distance & displacement | ⭐⭐⭐⭐⭐ |
| Speed & velocity | ⭐⭐⭐⭐⭐ |
| Average speed | ⭐⭐⭐⭐⭐ |
| Average velocity | ⭐⭐⭐⭐⭐ |
| Acceleration & retardation | ⭐⭐⭐⭐⭐ |
| Equations of motion | ⭐⭐⭐⭐⭐ |
| Velocity-time graph | ⭐⭐⭐⭐⭐ |
| Free fall / Galileo's laws | ⭐⭐⭐⭐⭐ |
| Chase/two-body problems | ⭐⭐⭐⭐⭐ |
📅 Year-wise Board Question Highlights
- 2016: Motion, acceleration, gravity, falling bodies, numerical application of equations of motion.
- 2017 Dhaka: Deer and tiger chase problem (80 kg deer at 72 km/h, tiger starting 75 m behind accelerating at 1.5 m/s²).
- 2020 Dhaka: Velocity-time graph analysis with acceleration calculation (2 m/s² from 0–40 m/s over 20 s).
- 2022: Equations of motion, graph-based problems, acceleration, falling bodies.
- 2023: Recurring areas — equations of motion, graphs, free fall, numerical problems.
- 2024: Bullet penetration problems, distance-time graphs, two-car relative motion.
- 2025 Dhaka: Two-car problem — one accelerating from rest (2.5 m/s²), another at 63 km/h from 50 m behind.
🎯 TOP 10 Must-Solve Problems for SSC
- Distance vs Displacement
- Speed vs Velocity
- Average Speed calculation
- Average Velocity calculation
- Acceleration from u, v, t
- All three equations of motion
- Velocity-time graph interpretation
- Two-car/chase problem
- Free-fall numerical (g = 9.8 m/s²)
- Galileo's three laws of falling bodies
Mathematical Problems with Solutions
These worked examples follow the NCTB patterns and board question style. Click to expand each solution.
Important Short Questions (SQ) — Board Style
Click on each question to reveal the answer.
Creative Questions (CQ) with Solutions
Key creative questions that frequently appear in board exams.
Graphs in Motion — Slope & Area
Understanding graphs is essential for board exams. Learn how to interpret position-time and velocity-time graphs.
📈 Position-Time Graph
- Slope = velocity
- Horizontal line = object at rest
- Straight sloping line = uniform velocity
- Curved line = accelerated motion
📉 Velocity-Time Graph
- Slope = acceleration
- Area under curve = displacement/distance
- Horizontal line = uniform velocity (zero acceleration)
- Sloping line = uniform acceleration
| Graph Type | Slope Gives | Area Gives |
|---|---|---|
| Position-Time | Velocity | — |
| Velocity-Time | Acceleration | Displacement |
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