Ch 02: Motion | Exam Fusion Prep

🏃 What is Motion?

Change in position of an object with time is called motion
e.g. Bird flying, Flowing water, Bus moving on road

(A) Motion Based on Nature of Path

Type	Meaning	Examples
Straight Line Motion	Particle moving in a straight line	Running child, Car on straight road
Rotational Motion	Body rotating on its axis in circular path	Motion of fan, Bicycle wheel
Oscillatory Motion	Back and forth about a fixed point / mean position	Pendulum in clock, Needle of sewing machine

(B) Motion Based on Dimensions

Type	Meaning	Axes	Examples
1D Motion	Variation of ONE coordinate with time	x-axis only	Car on straight road
2D Motion	Variation of TWO coordinates with time	x and y axes	Projectile motion, Circular motion, Planet revolving around sun
3D Motion	Variation of THREE coordinates with time	x, y, and z axes	Motion of mosquito, Bird, Water molecules

⚠ Exam Trap

Projectile motion = 2D (not 3D). Circular motion = 2D. Mosquito flying = 3D. Car on straight road = 1D.

⚖️ Uniform vs Non-Uniform Motion

Uniform Motion

Equal distance covered in equal time intervals
s-t graph = straight line through origin
Slope = constant

Non-Uniform Motion

Unequal distance covered in equal time intervals
s-t graph = curved line

📏 Distance vs Displacement

Feature	Distance (d)	Displacement (x)
Meaning	Length of path covered	Shortest path between initial & final position
Quantity	Scalar	Vector
Unit	meter (m)	meter (m)
Value	Always positive (+)	Positive, Negative, or Zero
Formula	Length of path	Final position − Initial position

⚠ Exam Trap

If object goes A→B (50m) then B→A (50m): Distance = 100m but Displacement = 0m. Distance can NEVER be zero if object moves, but displacement CAN be zero!

⚡ Speed vs Velocity

Feature	Speed (v)	Velocity (v)
Meaning	Distance covered in unit time	Displacement per unit time (with direction)
Quantity	Scalar	Vector
Unit	m/s	m/s
Value	Always positive	Positive, Negative, Zero
Formula	Distance ÷ Time	Displacement ÷ Time
Average	Total distance ÷ Total time	Total displacement ÷ Total time

🔥 Acceleration

Rate of change of velocity
Quantity: Vector | Unit: m/s²
Value: Positive, Negative, or Zero
Negative acceleration = Deceleration / Retardation

a = Δv / Δt = (v − u) / t

Average a = (v₂ − v₁) / (t₂ − t₁)

⚡ Worked Example

Car from rest (u=0) to 60 km/h in 20s: v = 60 × 5/18 = 50/3 m/s
a = (50/3 − 0) / 20 = 5/6 m/s²

📐 Equations of Motion — Straight Line

Initial velocity

Final velocity

Acceleration

Time

Displacement

1st Equation

Velocity-Time

v = u + at

2nd Equation

Position-Time

s = ut + ½at²

3rd Equation

Position-Velocity

v² = u² + 2as

🌏 Equations of Motion — Vertical (Free Fall)

Replace a with g (acceleration due to gravity) and s with h (height)

v = u + gt

h = ut + ½gt²

v² = u² + 2gh

⚡ Worked Example — Deceleration

Bullet: u=350 m/s, v=0, s=5 cm=0.05 m
Using v²=u²+2as → 0 = 350² − 2a(0.05)
a = 12.25 × 10⁵ m/s² (deceleration)

📊 Graph Slope Key Rules

Distance-Time Graph

Slope = Speed

Displacement-Time Graph

Slope = Velocity

Velocity-Time Graph

Slope = Acceleration
Area under graph = Displacement

📈 Position-Time (s-t) Graph

Graph Shape	Motion Type	Condition
Horizontal line (parallel to time axis)	State of Rest	v = 0
Straight line with positive slope	Uniform motion	s = ut
Upward curve (concave up)	Uniform accelerated motion	u = 0, s = ½at²
Downward curve (concave down)	Uniform decelerated motion	s = ut − ½at²

📉 Velocity-Time (v-t) Graph

Graph Shape	Motion Type	Condition
Horizontal line (parallel to time axis)	Uniform motion	v = const, a = 0
Straight line with positive slope	Uniform accelerated motion	a = const, v = at
Straight line with negative slope	Uniform decelerated motion	v = u − at
Upward curve	Non-uniform accelerated motion	—

⚠ Exam Trap

Slope of s-t graph = Speed/Velocity. Slope of v-t graph = Acceleration. Area under v-t graph = Displacement. Horizontal line in s-t graph = REST (not uniform motion!).

🎯 Projectile Motion

Body thrown at angle θ with horizontal → moves in curved parabolic path
Two-dimensional motion
Path is parabolic

Examples:Bomb from aeroplane, Ball hit by bat, Cannon ball, Rocket after fuel exhausted

📐 Projectile Formulas

Time of Flight (T)

T = 2u sinθ / g

Maximum Height (H)

H = u² sin²θ / 2g

Range (R)

R = u² sin 2θ / g

Special Angle Conditions

At θ = 90° → Maximum Height
At θ = 45° → Maximum Range
R_max = 4 × H_max

Key Properties

Horizontal velocity = constant (no air resistance)
Vertical velocity = changes due to gravity
At highest point: vertical velocity = 0

⚠ Exam Trap

θ = 45° → Maximum Range (NOT maximum height!). θ = 90° → Maximum Height. R_max = 4 × H_max — ye formula direct MCQ mein aata hai. Projectile path = Parabola.

🔄 Circular Motion

Motion of a body on a circular path
Uniform circular motion: Speed constant, velocity variable
Non-uniform circular motion: Speed and velocity both variable
e.g. Electron around nucleus, Moon around Earth

⚠ Exam Trap

Uniform circular motion mein speed constant hoti hai lekin velocity constant nahi (direction changes constantly!). So it IS accelerated motion even at constant speed!

📐 Components of Circular Motion

Component	Formula	Unit
Angular Displacement (θ)	θ = Arc (Δs) / Radius (r)	Radian
Angular Velocity (ω)	ω = Δθ / Δt	radian/second (rad/s)
Linear ↔ Angular relation	v = ωr = 2πnr	m/s
Angular Acceleration (α)	α = ω / t	rad/s²
Centripetal Acceleration (a)	a = v²/r = rω²	m/s² (always towards centre)

⚡ Quick Recall

Centripetal acceleration always points towards the centre. Centrifugal force = outward (pseudo force). v = ωr is the key relation between linear and angular velocity.

📋 Motion — Master Comparison

Quantity	Scalar/Vector	Unit	Formula
Distance	Scalar	m	Path length
Displacement	Vector	m	Final − Initial position
Speed	Scalar	m/s	d/t
Velocity	Vector	m/s	x/t
Acceleration	Vector	m/s²	(v−u)/t
Angular velocity	Vector	rad/s	θ/t
Angular acceleration	Vector	rad/s²	ω/t

🚀 Chapter 02 — Motion