The River of Motion

NODE 01

Idea of Motion

[FRAME]

• Rest and motion are relative.
• Motion compared with respect to what?
• Frame of reference is essential.

NODE 02

Position

• Location in space relative to an origin.
• Positive and negative direction.
• Position tells WHERE the object is.

NODE 03

Distance

• Total path length covered.
• Scalar quantity (cannot be negative).
• Distance tells HOW MUCH path is covered.

NODE 04

Displacement

• Change in position (Initial → Final).
• Vector nature (magnitude + direction).
• Displacement ≤ Distance.

NODE 05

Speed

• Distance / time (Scalar).
• Average vs Instantaneous speed.
• Speed asks "how fast?"

NODE 06

Velocity

• Displacement / time (Vector).
• Uniform vs Variable velocity.
• Velocity asks "how fast and in what direction?"

NODE 07

Acceleration

• Change in velocity (a = Δv / Δt).
• Positive acceleration vs Deceleration/Retardation.
• Motion becomes dynamic.

NODE 08

Motion Diagrams

• Position snapshots (ticker tape).
• Equal intervals = Uniform motion.
• Increasing gaps = Acceleration.

NODE 09

Types of Motion

• Translational (Rectilinear, Curvilinear).
• Rotational, Oscillatory, Periodic.
• Motion is a large family.

NODE 10

Uniform Motion

• Equal distances in equal intervals.
• Constant velocity in straight-line motion.
• Zero acceleration.

NODE 11

Non-Uniform Motion

• Unequal distances in equal intervals.
• Changing speed or velocity.
• Implies acceleration exists.

NODE 12

x-t Graph

• Position-Time Graph.
• Slope = Velocity.
• Straight line = Uniform motion.

NODE 13

v-t Graph

• Velocity-Time Graph.
• Slope = Acceleration.
• Area under graph = Displacement.

NODE 14

a-t Graph

• Acceleration-Time Graph.
• Area under graph = Change in velocity (Δv).

NODE 15

Equations of Motion

v = u + ats = ut + ½at²v² = u² + 2as

• For uniformly accelerated motion.
• Understand conditions and unit consistency.
• Do not merely memorize.

NODE 16

Sign Convention

+-

• Choosing positive/negative direction.
• Crucial for displacement, velocity, acceleration.
• Prevents massive calculation errors.

NODE 17

Free Fall

• Motion solely under gravity.
• Acceleration due to gravity (g).
• Symmetry of ideal vertical motion.

NODE 18

Motion Under Gravity

g = 9.8↓

• g ≈ 9.8 m/s² (approx 10 m/s²).
• Time of flight, maximum height.
• Kinematics before deep gravitational theory.

NODE 19

Relative Motion

• One object relative to another.
• Same-direction vs Opposite-direction.
• Moving observers (Train/River problems).

NODE 20

Uniform Circular

• Constant speed, but changing direction.
• Therefore, changing velocity = acceleration exists!
• Deeper mechanics in Realm 05.

NODE 21

Projectile Preview

• Horizontal component + Vertical component.
• Curved trajectory under gravity.
• Independence of horizontal/vertical motion.

NODE 22

Motion in Real Life

• Walking, cars, trains, planets.
• Translate: Real event → Model → Equation → Graph.

NODE 23

Problem Solving

• 1. Object 2. Frame 3. Knowns 4. Sign.
• 5. Goal 6. Equation 7. Units 8. Calculate.
• 9. Check sign 10. Physical reasonableness.

NODE 24

Motion Experiments

• Measuring speed, Trolley motion.
• Ticker tape, acceleration timing.
• Doing physics, not just reading it.

NODE 25

Mathematical Lang

x→v→a

• Position → Displacement → Velocity → Accel.
• The conceptual bridge toward calculus-based mechanics.

NODE 26

Calculus Frontier

v = dx/dt

a = dv/dt

• Preview for advanced physics.
• Velocity is the derivative of position.
• Acceleration is the derivative of velocity.

NODE 27

Misconceptions

v=0 ∴ a=0

X

• "v=0 means a=0" → False (e.g. apex of throw).
• "Negative a means slowing down" → Not necessarily.
• Explicitly attacking bad intuition.

NODE 28

Motion Vocabulary

• Position, Distance, Displacement, Speed, Velocity.
• Acceleration, Reference Frame, Trajectory.

NODE 29

The Master Rel.

POSITION↓ changeVELOCITY↓ change / timeACCEL

• The entire realm collapsed into one conceptual chain.
• Graphs → Slopes → Physical meaning.

NODE 30

Exit Gate

• We can describe motion, but not explain it yet.
• WHY does motion change?
• Opens REALM 03: The Vector Gate.