Relative Motion Engine

Purpose

Relative Motion is one of the most powerful shortcuts in kinematics.

Instead of analysing two moving objects separately, we convert the problem into a single-object motion problem.

Two Motions
↓
One Relative Motion
↓
Easy Solution

Golden Insight

Most Relative Motion problems become ordinary Distance-Speed-Time problems after choosing the correct observer.

6.1 Master Recognition Rule

Whenever you see the following trigger words:

Relative Velocity
Overtake
Catch Up
Separation
Approaching
Moving Towards Each Other
Train Crossing
Boat and Swimmer
Observer Frame

Immediate Thought

Use Relative Velocity

Recognition Shortcut

Two Moving Objects
↓
One Observer
↓
Relative Velocity

6.2 Relative Motion DNA

Relative Motion is not absolute motion.

It depends on who is observing.

Motion Seen By Observer

Example

Car A moves rightward at:

20 m/s

Car B moves rightward at:

15 m/s

An observer sitting in Car B sees Car A moving at:

5 m/s Rightward

Common Mistake

Students often use ground-frame velocity.

Relative Motion always depends on the chosen observer.

6.3 Fundamental Equation

Master Formula:

$$v_{AB}=v_A-v_B$$

Read As

Velocity of A
With Respect to B

Golden Rule

To find relative velocity:

Object Velocity
−
Observer Velocity

Memory Shortcut

Subtract Observer

Always subtract the velocity of the observer.

Master Question

Before solving any Relative Motion problem, ask:

Who is watching whom?

6.4 Same Direction Motion

Recognition Trigger

Both objects move in same direction
Faster object behind slower object
Car chasing another car
Overtaking situations

Relative Speed Formula

$$v_{rel}=|v_1-v_2|$$

Recognition Shortcut

Same Direction
↓
Subtract Speeds

Example

Car A = 60 km/h

Car B = 40 km/h

$$v_{rel}=60-40$$

$$v_{rel}=20\ km/h$$

Exam Trap

Many students add speeds.

For same-direction motion, always subtract.

6.5 Opposite Direction Motion

Recognition Trigger

Moving towards each other
Moving away from each other
Head-on motion
Approaching objects

Relative Speed Formula

$$v_{rel}=v_1+v_2$$

Recognition Shortcut

Opposite Directions
↓
Add Speeds

Example

Car A = 40 km/h

Car B = 60 km/h

$$v_{rel}=40+60$$

$$v_{rel}=100\ km/h$$

Exam Trap

Students often subtract speeds.

For opposite-direction motion, always add speeds.

6.6 Overtaking Engine

Recognition Trigger

Catch Up
Overtake
Faster object behind slower object
Pursuit Problems

Core Formula

$$t=\frac{Initial\ Separation}{Relative\ Speed}$$

Recognition Chain

Same Direction
↓
Subtract Speeds
↓
Relative Speed
↓
Time = Distance ÷ Relative Speed

Example

Faster car = 30 m/s

Slower car = 20 m/s

Initial separation = 100 m

$$v_{rel}=30-20$$

$$v_{rel}=10m/s$$

$$t=\frac{100}{10}=10s$$

Overtaking Shortcut

Overtake
↓
Relative Speed
↓
Distance / Relative Speed

6.7 Separation Engine

Recognition Trigger

Question asks:

How Far Apart?

Core Formula

$$Separation=(Relative\ Speed)\times Time$$

Recognition Chain

Relative Motion
↓
Convert to One Object
↓
Apply
Distance = Speed × Time

Example

Relative Speed = 15 m/s

Time = 20 s

$$Separation=15\times20$$

$$Separation=300m$$

Golden Insight

Relative Motion problems become ordinary Distance-Speed-Time problems after converting them into one-body motion.

6.8 Crossing Engine

Recognition Trigger

Train Crossing Pole
Train Crossing Platform
Train Crossing Train

Case 1: Train Crossing Pole

Pole has negligible length.

$$t=\frac{Length\ of\ Train}{Speed}$$

Case 2: Train Crossing Platform

Entire train must clear the entire platform.

$$t=\frac{Train\ Length+Platform\ Length}{Speed}$$

Case 3: Train Crossing Train

First calculate:

Relative Speed

Then apply:

$$t=\frac{Total\ Length}{Relative\ Speed}$$

Most Common Mistake

Students forget that the entire train must completely clear the object.

6.9 Relative Velocity Graph Logic

Core Idea

Relative position graphs contain direct information about relative velocity.

Slope
↓
Relative Velocity

Zero Relative Velocity

Constant Separation

Both objects move together.

Positive Relative Velocity

Separation Increasing

Negative Relative Velocity

Separation Decreasing

Graph Shortcut

Increasing Separation
↓
Positive Relative Velocity

Decreasing Separation
↓
Negative Relative Velocity

6.10 Relative Motion Decision Table

Trigger Seen	Immediate Tool
Same Direction	Subtract Speeds
Opposite Direction	Add Speeds
Overtake	Relative Speed
Separation	Relative Speed × Time
Train Crossing Pole	Length / Speed
Train Crossing Platform	Total Length / Speed
Relative Graph	Use Slope

Top Exam Traps

Trap 1

Adding Speeds in Same-Direction Motion

Trap 2

Subtracting Speeds in Opposite-Direction Motion

Trap 3

Using Ground Velocity instead of Relative Velocity

Trap 4

Ignoring Train Length

Trap 5

Ignoring Platform Length

Trap 6

Choosing Wrong Observer

One-Minute Revision Sheet

Same Direction
↓
Subtract Speeds

Opposite Direction
↓
Add Speeds

Overtaking
↓
Relative Speed
↓
Time = Distance / Relative Speed

Separation
↓
Relative Speed × Time

Crossing Pole
↓
Train Length / Speed

Crossing Platform
↓
(Train Length + Platform Length)
/ Speed

Crossing Train
↓
(Length₁ + Length₂)
/ Relative Speed

Golden Relative Motion Rule

Relative Motion is not about the object.

It is about the observer.

Always ask:

"Who is watching whom?"

Purpose

6.1 Master Recognition Rule

Immediate Thought

6.2 Relative Motion DNA

Example

6.3 Fundamental Equation

Read As

Golden Rule

Memory Shortcut

6.4 Same Direction Motion

Recognition Trigger

Relative Speed Formula

Recognition Shortcut

Example

6.5 Opposite Direction Motion

Recognition Trigger

Relative Speed Formula

Recognition Shortcut

Example

6.6 Overtaking Engine

Recognition Trigger

Core Formula

Recognition Chain

Example

6.7 Separation Engine

Recognition Trigger

Core Formula

Recognition Chain

Example

6.8 Crossing Engine

Recognition Trigger

Case 1: Train Crossing Pole

Case 2: Train Crossing Platform

Case 3: Train Crossing Train

6.9 Relative Velocity Graph Logic

Core Idea

Zero Relative Velocity

Positive Relative Velocity

Negative Relative Velocity

6.10 Relative Motion Decision Table

Top Exam Traps

One-Minute Revision Sheet

Continue Revision

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PYQ Masterclass