Every moving object around us — a falling apple, a speeding car, a planet orbiting the Sun, a blood cell rushing through a vein — is subject to the same fundamental laws of motion. Physics describes motion using precise quantities: distance (how far an object has traveled), displacement (how far it has moved from its start), speed (how fast), velocity (how fast and in what direction), and acceleration (how quickly velocity changes).
The mathematical description of motion — called kinematics — was first systematically studied by Galileo Galilei in the 17th century and formalized into the equations of motion we use today. These equations are the foundation of all of classical mechanics. For CBSE Class 9 Physics Chapter 8 (Motion), this is one of the most important and highest-scoring chapters in both school examinations and competitive tests. This guide covers all key subtopics: scalar and vector quantities, distance vs displacement, speed vs velocity, types of motion, acceleration, graphical analysis, derivation of all three equations of motion, uniform circular motion, and five solved numerical problems.
(no displacement s)
(no final velocity v)
(no time t)
- 1. Scalar and Vector Quantities
- 2. Distance vs Displacement
- 3. Speed vs Velocity
- 4. Types of Motion — Uniform, Non-uniform, Accelerated
- 5. Acceleration and Retardation
- 6. Distance-Time Graph and Velocity-Time Graph
- 7. Three Equations of Motion — Derivation and Use
- 8. Uniform Circular Motion
- 9. Solved Numerical Problems
- 10. Frequently Asked Questions (FAQ)
1. Scalar and Vector Quantities
Examples: Distance, speed, mass, time, temperature, energy, power, area, volume, density.
Arithmetic: Scalars add and subtract like ordinary numbers. E.g., if you walk 3 km North and then 3 km South, the distance traveled = 3 + 3 = 6 km (scalar addition).
Examples: Displacement, velocity, acceleration, force, momentum, weight, electric field, magnetic field.
Arithmetic: Vectors add by the vector addition law (triangle law or parallelogram law), not simple arithmetic. E.g., 3 km North + 3 km South = 0 displacement (vectors cancel).
2. Distance vs Displacement
• Always positive (or zero). Never negative.
• Can never decrease as the object moves.
• Depends on the actual path taken between two points.
Example: If a person walks 4 km East, then 3 km North, the distance = 4 + 3 = 7 km.
• Can be positive, negative, or zero.
• Can be zero even if distance is not (e.g., circular trip returning to start).
• Displacement ≤ Distance (always).
Example: 4 km East + 3 km North → Displacement = √(4²+3²) = √25 = 5 km (North-East).
| Property | Distance | Displacement |
|---|---|---|
| Type | Scalar (magnitude only) | Vector (magnitude + direction) |
| Definition | Total path length traveled | Shortest straight-line path from start to end |
| Symbol | d | s (or x, or Δx) |
| Sign | Always positive or zero | Can be positive, negative, or zero |
| Can be zero? | Only if object does not move | Yes — if object returns to starting point |
| Relation | Distance ≥ |Displacement| | |Displacement| ≤ Distance |
| Unit | metre (m) | metre (m) |
3. Speed vs Velocity
Unit: m/s (SI) or km/h
Average Speed: Total distance / Total time
Uniform Speed: Equal distances in equal time intervals
Example: A car that travels 100 km in 2 hours has an average speed of 50 km/h, regardless of direction.
Unit: m/s (SI) — with direction specified
Average Velocity: Total displacement / Total time
Uniform Velocity: Equal displacements in equal time intervals in the same direction
Example: A car going 50 km/h East has velocity = 50 km/h (East). The same car going 50 km/h West has velocity = -50 km/h (if East is positive).
4. Types of Motion
5. Acceleration and Retardation
a = (v − u) / t
where: u = initial velocity (m/s), v = final velocity (m/s), t = time taken (s), a = acceleration (m/s²)
Positive acceleration: Velocity is increasing (object speeding up) in the direction of motion.
Negative acceleration (retardation / deceleration): Velocity is decreasing (object slowing down). Acceleration is in the direction opposite to velocity.
Zero acceleration: Velocity is constant (uniform motion) OR object is at rest.
Uniform acceleration: Equal changes in velocity in equal time intervals. The velocity-time graph is a straight line. The three equations of motion are derived for uniform acceleration.
Non-uniform acceleration: Velocity changes by different amounts in equal time intervals. Velocity-time graph is a curve (not a straight line).
SI unit of acceleration: metre per second squared (m/s²). Other units: cm/s², km/h².
Standard acceleration due to gravity: g = 9.8 m/s² ≈ 10 m/s² (downward, toward Earth’s centre).
6. Distance-Time Graph and Velocity-Time Graph
📈 Distance-Time Graph (d-t graph)
• Slope = Speed: A steeper slope means greater speed.
• Horizontal line (slope = 0): Object is at rest (distance not changing with time).
• Straight line with positive slope: Uniform speed (equal distance in equal time).
• Upward curve (increasing slope): Speed is increasing (non-uniform, accelerated motion).
• Downward curve (decreasing slope): Speed is decreasing (non-uniform, decelerated motion).
Note: A d-t graph can never have a negative slope (distance never decreases).
📊 Velocity-Time Graph (v-t graph) — Most Important for CBSE
• Slope = Acceleration: Steep positive slope = large acceleration; negative slope = deceleration.
• Horizontal line (slope = 0): Uniform velocity (acceleration = 0).
• Straight line with positive slope: Uniform acceleration.
• Straight line with negative slope: Uniform retardation (deceleration).
• Area under the v-t graph = Displacement: For a rectangle (uniform v): s = v×t. For a triangle (uniform a from rest): s = ½×v×t. This is how the 2nd equation of motion is derived!
7. Three Equations of Motion — Derivation and Use
The three equations of motion apply to an object moving with uniform acceleration (constant acceleration a) in a straight line. Variables: u = initial velocity, v = final velocity, a = acceleration (constant), t = time, s = displacement.
Acceleration = Change in velocity / Time taken
a = (v − u) / t
Multiplying both sides by t:
at = v − u
Rearranging:
v = u + at
What it tells us: Given initial velocity u, acceleration a, and time t, find the final velocity v.
When to use: When displacement s is not required.
Special cases: u=0 (starts from rest): v = at. a=0 (uniform motion): v = u.
The displacement s = area under the v-t graph (trapezium with vertices at (0,u), (t,v), (t,0), (0,0)).
Area of trapezium = ½ × (sum of parallel sides) × height = ½ × (u + v) × t
Substituting v = u + at:
s = ½ × (u + u + at) × t = ½ × (2u + at) × t
s = ut + ½at²
What it tells us: Given u, a, and t, find the displacement s.
When to use: When final velocity v is not required.
Special cases: u=0 (starts from rest): s = ½at². a=0 (uniform motion): s = ut.
From 1st equation: t = (v − u)/a
Substituting into s = ½(u+v)t:
s = ½(u+v) × (v−u)/a = (v²−u²)/(2a)
Rearranging:
2as = v² − u²
v² = u² + 2as
What it tells us: Given u, a, and s, find final velocity v (or vice versa).
When to use: When time t is not given or required.
Special cases: u=0: v² = 2as → v = √(2as). a=0: v = u (uniform motion, v doesn’t change with distance).
8. Uniform Circular Motion
Is it accelerated? YES — even though the speed is constant, the direction of velocity changes continuously (velocity is always tangent to the circle). Since velocity (a vector) is changing, the object IS accelerating. This acceleration is directed toward the centre of the circle and is called centripetal acceleration (a⍾ = v²/r).
Key quantities:
• Speed (v) = constant = 2πr/T (circumference / period)
• Period (T) = time for one complete revolution
• Frequency (f) = 1/T (revolutions per second, Hz)
• Angular velocity (ω) = 2π/T = 2πf (radians per second)
• Centripetal force (F⍾) = mv²/r = mω²r (directed inward, toward centre)
Important note: In uniform circular motion, speed is constant but velocity is NOT constant (direction keeps changing). So the kinetic energy is constant, but momentum is not constant.
Examples of uniform circular motion:
• Earth orbiting the Sun (approximately circular orbit).
• Moon orbiting Earth.
• A satellite in circular orbit.
• A stone tied to a string and whirled in a horizontal circle.
• The tip of a clock hand (minute or second hand).
• A car going around a circular roundabout at constant speed.
9. Solved Numerical Problems
20 = 0 + a × 10
a = 20/10
Distance: s = ut + ½at² = 15×5 + ½×(-3)×25 = 75 − 37.5
Max height: v² = u² + 2as → 0 = (19.6)² + 2×(−9.8)×s
→ s = (19.6)² / (2×9.8) = 384.16/19.6
100 = 10×5 + ½×a×25
100 = 50 + 12.5a
12.5a = 50 → a = 4 m/s²
Final velocity: v = u + at = 10 + 4×5 = 10 + 20
Centripetal acceleration: a⍾ = v²/r = (10)²/70 = 100/70
Explore Related CBSE Class 9 Science Guides
10. Frequently Asked Questions (FAQ)
The three equations of motion for uniform acceleration are:
1st Equation: v = u + at (Velocity-Time relation)
2nd Equation: s = ut + ½at² (Displacement-Time relation)
3rd Equation: v² = u² + 2as (Velocity-Displacement relation)
Variables:
• u = initial velocity of the object (m/s)
• v = final velocity of the object (m/s)
• a = acceleration of the object (m/s²) — must be constant (uniform acceleration)
• t = time elapsed (s)
• s = displacement of the object during time t (m)
Which equation to use: Choose the equation that contains the three known quantities and the one unknown you need to find. If t is not given or needed, use the 3rd equation. If v is not given or needed, use the 2nd equation.
Distance is the total length of the path traveled by an object, regardless of direction. It is a scalar quantity (magnitude only). Distance is always positive or zero and can never decrease as an object moves.
Displacement is the shortest straight-line distance from the initial position to the final position of an object, in a specific direction. It is a vector quantity (magnitude + direction). Displacement can be positive, negative, or zero.
Key distinction: An object can have zero displacement while still having traveled a large distance. For example, if you walk 400 m around a circular track and return to your starting point, your distance = 400 m but your displacement = 0 m (same start and end point).
Relation: |Displacement| ≤ Distance. They are equal only when the motion is in a straight line in one direction without any reversal.
Speed is the distance traveled by an object per unit time. It is a scalar quantity (magnitude only, no direction). Speed is always positive. Formula: Speed = Distance/Time. Unit: m/s.
Velocity is the displacement of an object per unit time. It is a vector quantity (magnitude + direction). Velocity can be positive, negative, or zero. Formula: Velocity = Displacement/Time. Unit: m/s (with direction).
Example: A car driving in a circle at a constant 60 km/h has constant speed = 60 km/h, but its velocity is continuously changing (direction changes at every point).
Average speed vs average velocity: Average speed = Total distance / Total time. Average velocity = Total displacement / Total time. For a round trip (returning to start): average speed > 0 but average velocity = 0 (displacement = 0).
The slope (gradient) of a velocity-time graph represents the acceleration of the object.
Slope = Rise/Run = Change in velocity / Change in time = (v − u) / t = acceleration (a)
Interpreting v-t graph slopes:
• Positive slope (upward line): Positive acceleration (velocity increasing) — object speeding up in the positive direction.
• Zero slope (horizontal line): Zero acceleration (constant velocity) — uniform motion.
• Negative slope (downward line): Negative acceleration or retardation (velocity decreasing) — object slowing down.
Additionally: The area under the velocity-time graph equals the displacement of the object during that time interval. This is because area = velocity × time = displacement. For uniform velocity (rectangle): s = v × t. For uniformly increasing velocity (triangle): s = ½ × v × t. This is how the second equation of motion (s = ut + ½at²) is derived graphically.
Yes, uniform circular motion is accelerated motion, even though the speed is constant.
Reason: Acceleration is defined as the rate of change of velocity (not speed). Velocity is a vector quantity (it has both magnitude and direction). In uniform circular motion, the speed (magnitude of velocity) remains constant, but the direction of velocity continuously changes at every point along the circular path (velocity is always tangent to the circle). Since the direction of the velocity vector is changing, the velocity is changing — therefore, there IS acceleration.
This acceleration is called centripetal acceleration (a⍾ = v²/r), and it is directed toward the centre of the circle at every instant. The corresponding force keeping the object in circular motion is the centripetal force (F = mv²/r), also directed toward the centre.
Examples: A stone on a string whirled in a circle, the Moon orbiting Earth, a car turning around a curved road — all are accelerated even if speed is constant, because direction is continuously changing.
Source Motion & Mechanics Lab Equipment from Ambala
AJKANT Overseas manufactures and supplies ticker tape timers, inclined planes (with pulley and trolley), stopwatches, metre scales, vernier calipers, force meters (spring balances), mass sets, and complete CBSE Class 9 mechanics and motion practical lab kits. Factory-direct from Ambala, India. Trusted by schools, colleges, and government institutions across India and 25+ countries.
Request Mechanics Lab Equipment Quote →