What is a Frame of Reference?

Before studying motion in physics, we must answer one important question:

“Motion with respect to what?”

A body can appear to be at rest to one observer and in motion to another observer at the same time. Therefore, every measurement of position, velocity, or acceleration must be made relative to a Frame of Reference.

A Frame of Reference (FoR) is a coordinate system or reference point along with a clock from which an observer measures the position and motion of an object.

Simple Definition

A Frame of Reference is a system relative to which the position and motion of an object are observed and measured.

NCERT Definition

A frame of reference is a coordinate system attached to an observer with respect to which the position, displacement, velocity, and acceleration of an object are measured.

JEE Definition

A frame of reference is an imaginary three-dimensional coordinate system equipped with a clock, used to describe the motion of particles according to the laws of mechanics.

NEET Definition

A frame of reference is a point or coordinate system from which the motion of an object is observed.

Why Do We Need a Frame of Reference?

Imagine a train moving at 60 km/h.

A passenger sitting inside the train says,

“The person sitting next to me is not moving.”

A person standing on the platform says,

“The passenger is moving at 60 km/h.”

Who is correct?

Both are correct.

The difference arises because both observers are using different frames of reference.

Without specifying the frame of reference, statements such as

The car is moving.
The ball is at rest.
The bird is flying.

are incomplete.

Real-Life Examples of Frame of Refference

Example 1: Passenger Inside a Bus

A passenger sitting on a moving bus appears

At rest relative to another passenger
Moving relative to the road

Example 2: Airplane

A person sitting inside an airplane is

At rest with respect to the airplane
Moving with respect to Earth

Example 3: Earth

You are currently sitting on a chair.

Relative to your chair,

you are at rest.

Relative to the Sun,

you are moving because Earth rotates and revolves.

Example 4: Cricket Ball

A batsman sees the ball approaching.

A spectator sitting in the stadium also sees the ball approaching.

However, their measured position and velocity may differ depending upon their frame of reference.

Important Terms Related to Frame of Reference

Observer

An observer is the person who measures motion.

The observer chooses the frame of reference.

Object

The body whose motion is being studied.

Examples:

Car
Ball
Train
Rocket
Bicycle

Coordinate System

A coordinate system specifies the position of the object.

Usually,

X-axis
Y-axis
Z-axis

are used.

For JEE problems,

most questions use

One-dimensional motion
Two-dimensional motion

Clock

Every frame of reference also contains a clock because motion depends on time.

Without measuring time, velocity and acceleration cannot be calculated.

Components of a Frame of Reference

A complete frame of reference contains four things.

Position of Origin

The reference point from which measurements begin.

Example:

Suppose a railway station is chosen as the origin.

Distance of every train is measured from that station.

Coordinate Axes

Axes define directions.

Usually,

Positive X → Right
Positive Y → Upward
Positive Z → Outward

Observer

The person making observations.

Clock

Used for measuring time intervals.

Characteristics of a Good Frame of Reference

A good frame should

Have a fixed origin
Have properly defined axes
Include a clock
Allow accurate measurement of motion

Motion Depends on the Observer

This is one of the most important concepts in mechanics.

Consider a train moving at constant speed.

Observer A

Standing on the platform.

He observes

Train moving
Passenger moving
Luggage moving

Observer B

Sitting inside the train.

He observes

Passenger at rest
Luggage at rest
Platform moving backward

Same event.

Different observations.

Reason:

Different frames of reference.

Can an Object Be Both Moving and at Rest?

Yes.

This is possible because motion is relative.

Example

You are sitting inside a moving bus.

Relative to the bus

You are at rest.

Relative to the road

You are moving.

Relative to Earth

You are moving.

Relative to the Sun

You are moving even faster.

Therefore,

There is no absolute state of rest.

Absolute Motion vs Relative Motion

Absolute Motion

The concept of absolute motion assumes there exists a fixed point in the universe.

Modern physics does not support this idea.

Relative Motion

Motion is always measured relative to another object.

This concept is accepted in classical mechanics and modern physics.

Rest and Motion Are Relative

Rest

An object is said to be at rest if its position does not change with respect to the chosen frame of reference.

Motion

An object is said to be in motion if its position changes with respect to the chosen frame.

Important Note

The same object can simultaneously be

At rest
In motion

depending on the observer.

Mathematical Representation

Suppose

Object position

x=x(t)

where

x = position
t = time

If position changes with time,

\frac{dx}{dt}\neq0

the object is moving.

\frac{dx}{dt}=0

the object is at rest.

Notice that x is always measured relative to a frame of reference.

Everyday Examples of Relative Motion

Walking Inside a Train

Walking speed relative to train

= 2 m/s

Train speed relative to Earth

= 20 m/s

Walking speed relative to Earth

= 22 m/s (same direction)

18 m/s (opposite direction)

Boat Crossing a River

The boat’s speed relative to water differs from its speed relative to the riverbank because water itself is moving.

Escalator

Walking speed relative to escalator

is different from

walking speed relative to the building.

Conveyor Belt

A person standing on a moving conveyor belt is

At rest relative to belt
Moving relative to ground

Relative Motion Example Images

Common Misconceptions

Misconception 1

There is an object that is absolutely at rest.

Correct: There is no experimentally verified absolute frame of rest in classical mechanics.

Misconception 2

Motion is the same for everyone.

Correct: Motion depends on the observer’s frame of reference.

Misconception 3

If an object is moving, everyone measures the same velocity.

Correct: Velocity depends on the observer’s frame.

JEE & NEET Important Points

For NEET

Definition of frame of reference is frequently asked.
Understand observer-based motion.
Learn examples involving buses, trains, and airplanes.
Know that motion is always relative.

For JEE Main

Frame of reference forms the basis of kinematics.
Relative velocity questions directly depend on this concept.
Coordinate systems are important in problem-solving.

For JEE Advanced

Frame of reference is used extensively in relative motion, Newton’s laws, rotating frames, pseudo forces, and advanced mechanics.

Quick Revision

A frame of reference is used to describe motion.
Every motion is measured relative to an observer.
Motion and rest are relative concepts.
Different observers can describe the same event differently.
A complete frame of reference includes an origin, coordinate axes, an observer, and a clock.
There is no universally accepted absolute frame of rest in classical mechanics.
Relative motion is one of the foundational ideas in mechanics.

Frame of Refference : Part 2

Types of Frame of Reference

A frame of reference is not always the same. Depending on whether the observer is at rest, moving with constant velocity, or accelerating, the frame of reference is classified into two main types.

Inertial Frame of Reference
Non-Inertial Frame of Reference

Understanding these two frames is one of the most important topics in JEE Main, JEE Advanced, and NEET, as they form the foundation for Newton’s Laws of Motion, Relative Motion, Rotational Motion, and Advanced Mechanics.

Classification of Frames of Reference

Frame of Reference	Motion of Observer	Newton’s First Law Valid?	Pseudo Force Required?
Inertial Frame	At rest or moving with constant velocity	Yes	No
Non-Inertial Frame	Accelerating or rotating	No (unless pseudo force is added)	Yes

Inertial Frame of Reference

An Inertial Frame of Reference is a frame that is either at rest or moving with constant velocity (zero acceleration).

In such a frame, Newton’s Laws of Motion are directly applicable without any modification.

Definition

An inertial frame of reference is a frame in which an object remains at rest or continues to move with uniform velocity unless acted upon by an external force.

This definition is directly based on Newton’s First Law of Motion.

Understanding the Concept

Suppose a train moves in a straight line at a constant speed of 60 km/h.

Inside the train:

A ball placed on the floor remains at rest.
A hanging lamp hangs vertically.
A passenger feels normal.

The passenger cannot determine whether the train is moving or stationary without looking outside.

Therefore, the train behaves like an inertial frame because its velocity is constant.

Characteristics of an Inertial Frame

No Acceleration

The frame has zero acceleration.

a = 0

Velocity May Be Zero or Constant

The observer may be

Standing still
Moving with constant velocity

Both are inertial.

Newton’s Laws Are Valid

All three Newton’s laws can be applied directly.

No additional force is required.

Objects Behave Naturally

If no external force acts,

Rest remains rest.
Uniform motion remains uniform.

Mathematical Condition

\vec{a}_{frame}=0

then the frame is inertial.

Examples of Inertial Frames

Example 1: Person Standing on the Ground

For most school-level problems, Earth is approximately treated as an inertial frame because its rotation effects are very small.

Example 2: Train Moving with Constant Speed

If acceleration is zero,

the train becomes an inertial frame.

Example 3: Car on a Straight Highway

A car moving at a constant speed on a straight road is approximately an inertial frame.

Example 4: Spacecraft Moving in Deep Space

A spacecraft moving with constant velocity far away from gravitational influences behaves as an excellent inertial frame.

Image of Inertial Frame

Prompt:

Create a textbook-quality educational illustration showing a train moving on a straight railway track with constant velocity toward the right. Inside the train, a passenger is seated comfortably, a ball rests on the floor, and a hanging lamp hangs vertically without tilting. Outside the train, arrows indicate “Constant Velocity” and “Acceleration = 0”. Add labels: “Inertial Frame”, “Newton’s Laws Applicable”, and “No Pseudo Force”. Use a clean vector style, white background, blue and gray color palette, NCERT/JEE physics textbook appearance, 16:9 aspect ratio.

Newton’s First Law and Inertial Frames

Newton’s First Law states:

An object remains at rest or continues to move with uniform velocity unless acted upon by an external unbalanced force.

This law is valid only in an inertial frame of reference.

If the observer is accelerating, Newton’s First Law appears to fail unless an additional force (pseudo force) is introduced.

Why Is It Called an Inertial Frame?

The word inertia means the tendency of an object to resist changes in its state of motion.

Since objects naturally exhibit inertia in these frames, they are called inertial frames.

Important Observation

If Newton’s First Law is satisfied,

the frame is inertial.

If Newton’s First Law appears to fail,

the frame is probably non-inertial.

This is a common conceptual question in JEE Advanced.

Non-Inertial Frame of Reference

A Non-Inertial Frame of Reference is a frame that is accelerating or rotating relative to an inertial frame.

In such a frame, Newton’s Laws do not hold unless an additional imaginary force called the pseudo force is included.

Definition

A non-inertial frame is a frame undergoing acceleration or rotation in which Newton’s Laws cannot be applied directly.

Why Do Newton’s Laws Fail?

Imagine standing inside a bus.

The bus suddenly accelerates forward.

Without anyone pushing you,

you feel as if you are thrown backward.

Actually,

your body tends to remain in its original state due to inertia.

The backward feeling is explained using a pseudo force in the accelerating frame.

Characteristics of a Non-Inertial Frame

Frame Has Acceleration

a \neq 0

Newton’s Laws Are Not Directly Applicable

Additional forces must be introduced.

Pseudo Force Appears

This force is not caused by any physical interaction.

It appears only because the observer is accelerating.

Observer Experiences Apparent Motion

Objects may appear to move even when no real force acts on them.

Mathematical Condition

\vec{a}_{frame}\neq0

the frame is non-inertial.

Examples of Non-Inertial Frames

Accelerating Bus

When the bus starts suddenly,

passengers feel pushed backward.

Suddenly Braking Car

When the brakes are applied,

passengers feel pushed forward.

Elevator

When the elevator accelerates upward,

your apparent weight increases.

When it accelerates downward,

your apparent weight decreases.

Merry-Go-Round

A rotating platform is a non-inertial frame because the direction of velocity continuously changes.

Rocket Launch

A rocket accelerating upward forms a non-inertial frame.

Pseudo Force (Fictitious Force)

A Pseudo Force is an imaginary force introduced in a non-inertial frame so that Newton’s Laws remain valid for an observer in that frame.

It is also called:

Fictitious Force
Inertial Force
Apparent Force

Definition

A pseudo force is a force that appears due to the acceleration of the observer and not because of any physical interaction between objects.

Formula for Pseudo Force

If a frame accelerates with acceleration a, then for an object of mass (m):

\boxed{\vec{F}{\text{pseudo}} = -m\vec{a}{\text{frame}}}

The negative sign indicates that the pseudo force acts opposite to the acceleration of the frame.

Direction of Pseudo Force

Frame Acceleration	Direction of Pseudo Force
Forward	Backward
Backward	Forward
Upward	Downward
Downward	Upward
Left	Right
Right	Left

Why Is It Called an Imaginary Force?

Unlike gravity or friction, a pseudo force:

Has no physical source.
Does not arise from interaction between two bodies.
Exists only for an observer in a non-inertial frame.

An observer in an inertial frame does not include this force.

Real-Life Examples of Pseudo Force

Passenger in a Bus

When the bus accelerates,

you feel pushed backward.

The actual cause is your body’s inertia, but in the accelerating frame this effect is represented by a pseudo force.

Elevator

When the elevator accelerates upward,

the pseudo force acts downward, making you feel heavier.

Rotating Carousel

A rider feels pushed outward.

This apparent outward force is the centrifugal pseudo force.

pseudo force explaining accelerated motion in a non-inertial frame

Difference Between Inertial and Non-Inertial Frames

Feature	Inertial Frame	Non-Inertial Frame
Acceleration	Zero	Non-zero
Velocity	Constant	Changing
Newton’s Laws	Directly applicable	Need pseudo force
Pseudo Force	Not required	Required
Observer	At rest or constant velocity	Accelerating or rotating
Examples	Stationary ground, constant-speed train	Accelerating bus, rotating platform, elevator

How to Identify the Frame in JEE Questions

Step 1

Check whether the observer is accelerating.

If No, the frame is inertial.
If Yes, continue to Step 2.

Step 2

Determine whether Newton’s Laws are applied directly.

If yes, inertial frame.
If pseudo force must be added, non-inertial frame.

Step 3

Look for common keywords.

Inertial Frame Keywords

Constant velocity
Uniform motion
Stationary
Straight line with constant speed

Non-Inertial Frame Keywords

Accelerating
Retarding
Rotating
Circular motion
Elevator
Rocket
Accelerating bus
Braking train

JEE Advanced Insight

A frame moving with constant velocity relative to another inertial frame is also an inertial frame. This principle forms the basis of Galilean Relativity, which will be discussed in the next part.

NEET/JEE Quick Revision

Motion is measured relative to a frame of reference.
Two types of frames: Inertial and Non-Inertial.
Inertial frames have zero acceleration.
Newton’s Laws work directly only in inertial frames.
Non-inertial frames are accelerating or rotating.
Pseudo force is introduced only in non-inertial frames.
Formula of pseudo force:

\boxed{F_{\text{pseudo}} = -ma_{\text{frame}}}

Frame of Refference : Part 3

Relative Motion in Different Frames of Reference

One of the most important applications of the Frame of Reference is the study of Relative Motion. Almost every JEE Main, JEE Advanced, and NEET mechanics problem involving trains, boats, airplanes, rain, wind, or moving observers is based on this concept.

The central idea is:

The motion of an object depends on the observer who is measuring it.

For example, a passenger sitting inside a moving train may appear stationary to another passenger but moving to a person standing on the platform.

What is Relative Motion?

Relative motion is the motion of one object as observed from another moving or stationary object.

In simple words,

Relative motion tells us how fast one object appears to move with respect to another object.

Definition

The motion of an object measured with respect to another moving or stationary object is called relative motion.

Why is Relative Motion Important?

Relative motion helps us solve problems involving:

Moving trains
Boats crossing rivers
Airplanes flying in wind
Rain appearing inclined
Escalators
Conveyor belts
Moving elevators
Relative speed of two particles

Without relative motion, many mechanics problems cannot be solved correctly.

Relative Position

Before understanding relative velocity, we must first understand relative position.

Suppose:

Object A is at position (x_A)
Object B is at position (x_B)

The position of A relative to B is

\boxed{\vec r_{AB}=\vec r_A-\vec r_B}

Similarly,

The position of B relative to A is

\boxed{\vec r_{BA}=\vec r_B-\vec r_A}

Notice that

\boxed{\vec r_{AB}=-\vec r_{BA}}

This means the relative position vectors have the same magnitude but opposite directions.

Example

Car A is at 20 m

Car B is at 50 m

Then Relative position of A with respect to B

r_{AB}=20-50=-30,m

The negative sign indicates that A is 30 m behind B.

Relative Velocity

Relative velocity is one of the most frequently tested concepts in JEE.

Definition

Relative velocity is the velocity of one object measured with respect to another object.

Mathematical Formula

Velocity of A = (\vec v_A)
Velocity of B = (\vec v_B)

Velocity \\of\\ A = (\vec v_A)

Velocity \\of\\ B = (\vec v_B)

Then,

Velocity of A relative to B is

\boxed{\vec v_{AB}=\vec v_A-\vec v_B}

Similarly,

\boxed{\vec v_{BA}=\vec v_B-\vec v_A}

Hence,

\boxed{\vec v_{AB}=-\vec v_{BA}}

Physical Meaning

Suppose:

Car A moves at 40 km/h

Car B moves at 30 km/h

Both move in the same direction.

Relative velocity = 40-30=10 km/h

A appears to move only 10 km/h faster than B.

Cases of Relative Velocity

Case 1: Both Objects Move in the Same Direction

Formula

\boxed{v_{relative}=v_1-v_2}

Take the difference of speeds.

Example

Train A : 80 km/h

Train B : 60 km/h

Same direction Relative speed = 80-60=20 km/h

Case 2: Objects Move in Opposite Directions

Formula

\boxed{v_{relative}=v_1+v_2}

The speeds are added.

Example

Train A : 70 km/h

Train B : 90 km/h

Opposite directions

Relative speed = 70+90=160 km/h

Case 3: One Object is Stationary

If v_B=0

Then v_AB=v_A

This is why stationary observers measure the actual speed of moving objects.

Relative Acceleration

Just as velocity can be relative, acceleration can also be relative.

Formula

Acceleration of A

\vec a_A

Acceleration of B

\vec a_B

Then

Relative acceleration

\boxed{\vec a_{AB}=\vec a_A-\vec a_B}

Special Case

If both bodies have equal acceleration,

a_A=a_B

then

a_{AB}=0

Their relative velocity remains constant.

Derivation of Relative Velocity Formula

Suppose

Position vector of A

\vec r_A

Position vector of B

\vec r_B

Relative position

\vec r_{AB}=\vec r_A-\vec r_B

Differentiate with respect to time

\frac{d\vec r_{AB}}{dt}

\frac{d\vec r_A}{dt}

\frac{d\vec r_B}{dt}

Since

\frac{d\vec r}{dt}

\vec v

Therefore

\vec v_{AB} = \vec v_A-\vec v_B

This derivation is important for JEE Advanced.

Galilean Transformation

Galilean Transformation relates the coordinates of the same event measured from two different inertial frames moving with constant velocity relative to each other.

It forms the basis of Classical Mechanics.

Assumptions

Both frames are inertial.
Relative velocity is constant.
Time is absolute.
Space is absolute.

Consider Two Frames

Frame S Stationary.

Frame S’ Moves with constant velocity v along the positive x-axis.

Coordinate Transformation

Suppose

An object has coordinates

[
(x,y,z,t)
]

in frame S.

Then in frame S’

\boxed{x’=x-vt}

\boxed{y’=y}

\boxed{t’=t}

These are called Galilean Transformation Equations.

Inverse Transformation

From moving frame to stationary frame

\boxed{x=x’+vt}

y=y’, z=z’, t=t’

Velocity Transformation

Differentiate

x’=x-vt

with respect to time.

\frac{dx’}{dt} = \frac{dx}{dt} = v

Therefore,

\boxed{v’_x=v_x-v}

Similarly,

v’_y=v_y

v’_z=v_z

Interpretation

The moving observer measures a velocity reduced by the frame’s velocity.

Acceleration Transformation

Differentiate once again.

Since

v=constant

its derivative becomes zero.

Therefore

\boxed{a’_x=a_x}

Similarly,

a’_y=a_y

a’_z=a_z

Important Result

Acceleration remains the same in all inertial frames.

This is why Newton’s Laws are valid in every inertial frame.

This is one of the most important theoretical questions in JEE.

Image Prompt – Galilean Transformation

Prompt:

Create a detailed educational physics diagram illustrating two inertial frames of reference. Frame S is stationary with X and Y axes. Frame S′ moves toward the positive X-direction with constant velocity v. Place a particle P between the frames and show its coordinates as (x, y) in frame S and (x′, y′) in frame S′. Draw arrows indicating the motion of frame S′ and label the equations x′ = x − vt, y′ = y, t′ = t. Use clean vector graphics, white background, textbook-quality design suitable for NCERT, JEE, and NEET, 16:9 aspect ratio.

Relative Motion of Two Particles

Suppose two particles move simultaneously.

Particle A

Velocity

[
\vec v_A
]

Particle B

Velocity

[
\vec v_B
]

Relative velocity

[
\boxed{\vec v_{AB}

\vec v_A-\vec v_B}
]

Relative acceleration

[
\boxed{\vec a_{AB}

\vec a_A-\vec a_B}
]

This concept is widely used in projectile motion and collision problems.

Boat and River Problems

Boat problems are among the most common applications of relative velocity.

Velocity Definitions

Boat relative to water
River relative to ground
Boat relative to ground

The vector equation is

[
\boxed{\vec v_{BG}

\vec v_{BW}
+
\vec v_{WG}}
]

where:

( \vec v_{BG} ) = velocity of the boat relative to the ground
( \vec v_{BW} ) = velocity of the boat relative to the water
( \vec v_{WG} ) = velocity of the water (river) relative to the ground

Always remember that velocities must be added as vectors, not just as numbers.

Rain-Man Problem

Another classic application of relative velocity is the rain-man problem.

Situation

A person is walking while rain falls vertically.

To the person, the rain appears to fall at an angle.

Reason:

The person’s own velocity changes the apparent direction of the rain.

This concept explains why you tilt an umbrella while walking.

Image Prompt – Rain-Man Relative Motion

Prompt:

Design a textbook-style educational diagram showing rain falling vertically toward the ground while a person walks toward the right. Draw three vectors: vertical rain velocity, horizontal walking velocity, and the resultant apparent rain velocity inclined toward the person. Label them clearly as “Velocity of Rain”, “Velocity of Man”, and “Apparent Velocity of Rain”. Include a tilted umbrella aligned with the apparent rain direction. Use a white background, clean vector illustrations, physics textbook style, suitable for JEE and NEET, 16:9 aspect ratio.

Common Mistakes Made by Students

Using Addition Instead of Subtraction

For objects moving in the same direction, students often add velocities instead of subtracting them.

Ignoring Direction

Velocity is a vector quantity. Always assign the correct sign and direction.

Confusing Speed with Velocity

Speed is scalar, while relative velocity depends on direction.

Using Galilean Transformation in Accelerating Frames

Galilean transformations are valid only for inertial frames moving with constant relative velocity.

JEE Advanced Concept

If two particles have:

Equal velocity
Equal acceleration

then

their relative velocity and relative acceleration are both zero.

Hence, the distance between them remains constant.

This idea is frequently used in advanced mechanics and pursuit problems.

NEET Quick Revision

Relative position:
[
\boxed{\vec r_{AB}=\vec r_A-\vec r_B}
]
Relative velocity:
[
\boxed{\vec v_{AB}=\vec v_A-\vec v_B}
]
Relative acceleration:
[
\boxed{\vec a_{AB}=\vec a_A-\vec a_B}
]
Same direction → subtract velocities.
Opposite directions → add speeds.
Galilean transformations apply only to inertial frames.
Time is absolute in Galilean relativity.
Acceleration is the same in all inertial frames.

Frame of Refference : Part 4

Solved Examples on Frame of Reference and Relative Motion (JEE & NEET Level)

Now that we have studied the theory of Frame of Reference, Inertial and Non-Inertial Frames, Pseudo Force, Relative Motion, and Galilean Transformation, it is time to apply these concepts to numerical problems.

This section begins with basic examples and gradually progresses to JEE Main, JEE Advanced, and NEET level questions.

Problem-Solving Strategy

Before solving any question on relative motion, always follow these steps:

Identify the frame of reference.

Write the given velocities with proper directions.

Convert all quantities into the same unit (preferably SI units).

Apply the appropriate relative velocity equation.

Check whether vector addition or subtraction is required.

Verify the direction of the final answer.

Example 1 – Passenger Inside a Moving Train

Question

A train moves with a constant velocity of 72 km/h. A passenger is sitting inside the train.

Find the velocity of the passenger:

Relative to the train
Relative to the ground

Solution

Train speed

[
v_{TG}=72;km/h
]

Passenger is sitting inside the train.

Therefore,

Passenger relative to train

[
v_{PT}=0
]

Passenger relative to ground

[
v_{PG}=72;km/h
]

Final Answer

Relative to train = 0 km/h
Relative to ground = 72 km/h

Concept Learned

A body can be at rest in one frame and moving in another frame simultaneously.

Example 2 – Two Cars Moving in the Same Direction

Question

Car A moves at 60 km/h.

Car B moves at 40 km/h.

Both move in the same direction.

Find the velocity of A relative to B.

Solution

Relative velocity

[
v_{AB}=v_A-v_B
]

Substitute values

[
v_{AB}=60-40
]

[
=20;km/h
]

Final Answer

[
\boxed{20;km/h}
]

Concept Learned

For motion in the same direction,

subtract the velocities.

Example 3 – Two Trains Moving in Opposite Directions

Question

Train A moves at 80 km/h.

Train B moves at 70 km/h.

They move toward each other.

Find their relative speed.

Solution

Opposite directions

[
v_{relative}=80+70
]

[
=150;km/h
]

Final Answer

[
\boxed{150;km/h}
]

Concept Learned

For opposite directions,

add the speeds.

Example 4 – Relative Velocity Using Vectors

Question

Object A moves east with velocity

[
10;m/s
]

Object B moves east with velocity

[
6;m/s
]

Find the velocity of A relative to B.

Solution

Take east as positive.

[
v_{AB}=10-6
]

[
=4;m/s
]

towards east.

Final Answer

[
\boxed{4;m/s;East}
]

Example 5 – Moving Observer

Question

A cyclist moves at 15 m/s.

An observer runs in the same direction at 5 m/s.

Find the cyclist’s velocity relative to the observer.

Solution

[
v_{CO}=15-5
]

[
=10;m/s
]

Final Answer

[
\boxed{10;m/s}
]

Example 6 – Relative Acceleration

Question

Particle A accelerates at

[
5;m/s^2
]

Particle B accelerates at

[
2;m/s^2
]

Find the acceleration of A relative to B.

Solution

[
a_{AB}=5-2
]

[
=3;m/s^2
]

Final Answer

[
\boxed{3;m/s^2}
]

Example 7 – Galilean Transformation

Question

A particle is at

[
x=120,m
]

[
t=5,s
]

Frame S′ moves with velocity

[
10,m/s
]

Find the coordinate of the particle in S′.

Solution

Use

[
x’=x-vt
]

Substitute

[
x’=120-(10)(5)
]

[
=120-50
]

[
=70,m
]

Final Answer

[
\boxed{70,m}
]

Example 8 – Constant Velocity Train

Question

A train moves at constant velocity.

A ball is placed on the floor.

Will the ball move relative to the train?

Solution

No.

The train is an inertial frame.

The ball remains at rest relative to the train.

Final Answer

The ball remains stationary inside the train.

Concept Learned

Objects at rest remain at rest in inertial frames unless acted upon by an external force.

Example 9 – Accelerating Bus

Question

A bus suddenly accelerates forward.

Why do passengers appear to move backward?

Solution

Passengers are not actually pushed backward.

Their bodies tend to remain in their original state of motion due to inertia.

To an observer inside the accelerating bus, this effect is represented by a pseudo force acting backward.

Final Answer

The backward motion is due to inertia, while the pseudo force explains the observation in the non-inertial frame.

Image Prompt – Passenger in an Accelerating Bus

Prompt:

Create a detailed educational illustration of a bus accelerating toward the right. Show passengers leaning backward due to inertia. Draw a forward arrow labeled “Bus Acceleration (a)” and a backward arrow labeled “Pseudo Force”. Include a hanging pendulum tilted backward. Add labels explaining that the bus is a non-inertial frame and that Newton’s laws require a pseudo force. Use a clean vector style, white background, textbook-quality graphics, 16:9 aspect ratio.

Example 10 – Elevator Moving Upward

Question

An elevator accelerates upward.

How does a passenger feel?

Solution

The normal reaction from the floor increases.

Therefore,

the passenger feels heavier.

Apparent weight

[
N=m(g+a)
]

Final Answer

The passenger feels heavier because the apparent weight increases.

Example 11 – Elevator Moving Downward

Question

An elevator accelerates downward.

What happens to the apparent weight?

Solution

Normal reaction decreases.

Apparent weight

[
N=m(g-a)
]

Final Answer

The passenger feels lighter.

Example 12 – Boat Crossing a River

Question

A boat moves with speed

[
6,m/s
]

relative to water.

The river flows at

[
4,m/s
]

perpendicular to the boat’s direction.

Find the speed of the boat relative to the ground.

Solution

Since the velocities are perpendicular,

use the Pythagorean theorem:

[
v=\sqrt{6^2+4^2}
]

[
=\sqrt{36+16}
]

[
=\sqrt{52}
]

[
\approx7.21,m/s
]

Final Answer

[
\boxed{7.21,m/s}
]

Image Prompt – Boat Crossing a River

Prompt:

Create a textbook-style physics diagram of a river flowing horizontally from left to right. Show a boat attempting to cross vertically. Draw three vectors: boat velocity relative to water (upward), river velocity (rightward), and resultant velocity relative to the ground (diagonal). Label each vector clearly and include the formula (v=\sqrt{v_b^2+v_r^2}). Use a clean white background and vector graphics suitable for NCERT, JEE, and NEET, 16:9 aspect ratio.

Example 13 – Rain-Man Problem

Question

Rain falls vertically at

[
8,m/s
]

A man walks horizontally at

[
6,m/s
]

Find the apparent speed of rain relative to the man.

Solution

Resultant velocity

[
v=\sqrt{8^2+6^2}
]

[
=\sqrt{64+36}
]

[
=\sqrt{100}
]

[
=10,m/s
]

Final Answer

[
\boxed{10,m/s}
]

Example 14 – Identifying the Frame

Question

A rotating merry-go-round is observed.

Is it an inertial frame?

Solution

No.

The direction of velocity changes continuously.

Therefore,

the frame has centripetal acceleration.

It is a non-inertial frame.

Final Answer

Rotating frames are non-inertial.

Example 15 – Earth as a Frame of Reference

Question

Is the Earth an inertial frame?

Solution

Strictly speaking,

No.

Earth rotates and revolves, so it has acceleration.

However,

for most school-level, NEET, and JEE Main problems,

Earth is treated as an approximately inertial frame because these accelerations are very small.

Final Answer

Earth is approximately inertial for most practical mechanics problems.

Mixed Conceptual Questions

Question 1

Can two objects have zero relative velocity even if both are moving?

Answer

Yes.

If both move with the same velocity in the same direction, their relative velocity is zero.

Question 2

Can an object have zero speed but non-zero acceleration?

Answer

Yes.

At the highest point of vertical upward motion, the speed is zero for an instant, but the acceleration due to gravity is still acting downward.

Question 3

Can a moving observer measure an object at rest?

Answer

Yes.

If the observer and the object move with the same velocity, the object appears at rest relative to the observer.

Question 4

Why is pseudo force called fictitious?

Answer

Because it has no physical source or interaction. It appears only when observations are made from a non-inertial frame.

Frequently Asked JEE & NEET Concepts

JEE Main

Relative velocity of trains
Boat crossing river
Rain-man problems
Accelerating lift
Constant velocity frames

JEE Advanced

Vector form of relative velocity
Galilean transformations
Multiple moving particles
Non-inertial frame analysis
Pseudo force applications
Rotating frames

NEET

Definitions
Inertial and non-inertial frames
Newton’s First Law
Apparent weight in lifts
Relative motion basics

Common Mistakes to Avoid

Forgetting Vector Directions

Relative velocity depends on direction, not just magnitude.

Mixing Units

Always convert km/h to m/s when required.

[
1;km/h=\frac{5}{18};m/s
]

Treating Accelerating Frames as Inertial

Whenever acceleration is present, check whether a pseudo force is required.

Ignoring the Frame of Reference

Always ask:

Relative to whom is the motion being measured?

This single question helps avoid many conceptual mistakes.

Chapter Summary (Part 4)

Solved problems reinforce the concepts of frame of reference and relative motion.
Relative velocity is found by vector subtraction.
Same-direction motion requires subtraction; opposite-direction motion requires addition.
Boat-river and rain-man problems use vector addition.
Pseudo force explains observations in non-inertial frames.
Earth is treated as an approximately inertial frame for most introductory mechanics problems.
Identifying the correct frame of reference is the first and most important step in solving any mechanics problem.

Frame of Refference : Part 5

JEE & NEET Practice Questions, Revision Notes, Formula Sheet, and Exam Preparation

This final part is designed as a complete revision module for JEE Main, JEE Advanced, and NEET. It consolidates all the concepts discussed in the previous parts and provides practice material to strengthen your understanding.

Important Formula Sheet

Before attempting questions, revise the most important formulas.

Relative Position

[
\boxed{\vec r_{AB}=\vec r_A-\vec r_B}
]

where

(\vec r_A) = Position vector of object A
(\vec r_B) = Position vector of object B

Relative Velocity

[
\boxed{\vec v_{AB}=\vec v_A-\vec v_B}
]

Relative Acceleration

[
\boxed{\vec a_{AB}=\vec a_A-\vec a_B}
]

Galilean Transformation

Coordinate Transformation

[
\boxed{x’=x-vt}
]

[
\boxed{y’=y}
]

[
\boxed{z’=z}
]

[
\boxed{t’=t}
]

Velocity Transformation

[
\boxed{v’_x=v_x-v}
]

Acceleration Transformation

[
\boxed{a’_x=a_x}
]

Acceleration remains unchanged in all inertial frames.

Pseudo Force

[
\boxed{\vec F_{pseudo}=-m\vec a_{frame}}
]

The pseudo force always acts opposite to the acceleration of the frame.

Apparent Weight in an Elevator

Elevator accelerating upward

[
\boxed{N=m(g+a)}
]

Elevator accelerating downward

[
\boxed{N=m(g-a)}
]

Free fall

[
\boxed{N=0}
]

Relative Speed

Same direction

[
\boxed{v_{relative}=v_1-v_2}
]

Opposite directions

[
\boxed{v_{relative}=v_1+v_2}
]

Complete Formula Summary Table

Concept	Formula
Relative Position	(\vec r_{AB}=\vec r_A-\vec r_B)
Relative Velocity	(\vec v_{AB}=\vec v_A-\vec v_B)
Relative Acceleration	(\vec a_{AB}=\vec a_A-\vec a_B)
Galilean Transformation	(x’=x-vt)
Velocity Transformation	(v’=v-v_f)
Pseudo Force	(F=-ma)
Elevator (Upward)	(N=m(g+a))
Elevator (Downward)	(N=m(g-a))

Multiple Choice Questions (MCQs)

MCQ 1

A train moves with constant velocity. Which type of frame does it represent?

A. Non-inertial

B. Rotating

C. Inertial

D. Accelerated

Answer: C

MCQ 2

Pseudo force exists only in

A. Stationary frame

B. Inertial frame

C. Non-inertial frame

D. Vacuum

Answer: C

MCQ 3

Two cars move in the same direction with speeds of 80 km/h and 60 km/h.

Relative speed equals

A. 20 km/h

B. 140 km/h

C. 80 km/h

D. 60 km/h

Answer: A

MCQ 4

The SI unit of relative velocity is

A. m

B. m/s

C. kg

D. N

Answer: B

MCQ 5

A frame accelerating upward is

A. Inertial

B. Non-inertial

C. Stationary

D. Absolute

Answer: B

MCQ 6

The formula for pseudo force is

A. (ma)

B. (-ma)

C. (mg)

D. (mv)

Answer: B

MCQ 7

Galilean transformations are applicable only between

A. Rotating frames

B. Accelerating frames

C. Inertial frames

D. Circular motion frames

Answer: C

MCQ 8

Acceleration is the same in all inertial frames because

A. Time changes

B. Relative velocity is zero

C. Relative acceleration between inertial frames is zero

D. Mass changes

Answer: C

MCQ 9

When two bodies move in opposite directions, their relative speed is obtained by

A. Multiplication

B. Division

C. Addition

D. Subtraction

Answer: C

MCQ 10

Which quantity changes with the observer?

A. Mass

B. Relative velocity

C. Charge

D. Density

Answer: B

Assertion–Reason Questions

Question 1

Assertion (A):

Newton’s First Law is valid only in inertial frames.

Reason (R):

In non-inertial frames, pseudo force must be introduced.

Answer

Both A and R are true, and R correctly explains A.

Question 2

Assertion

Earth is an inertial frame.

Reason

Earth rotates and revolves around the Sun.

Answer

Assertion is false (strictly speaking).

Reason is true.

Question 3

Assertion

Relative velocity may be zero even if two objects are moving.

Reason

Both objects may have the same velocity.

Answer

Both are true.

Numerical Practice Questions

Question 1

Two trains move in the same direction.

Train A = 90 km/h

Train B = 50 km/h

Find the relative speed.

Answer

40 km/h

Question 2

Two cars move toward each other.

60 km/h

40 km/h

Relative speed?

Answer

100 km/h

Question 3

A lift accelerates upward with

[
2m/s^2
]

Find the apparent weight of a

50 kg person.

(Take

[
g=10m/s^2
])

Solution

[
N=m(g+a)
]

[
=50(10+2)
]

[
=600N
]

Question 4

A frame accelerates rightward with

[
5m/s^2
]

Find the pseudo force on a

2 kg block.

Solution

[
F=-ma
]

[
=-2\times5
]

Magnitude

[
10N
]

Direction

Left

Question 5

A boat moves

5 m/s

relative to water.

River speed

12 m/s

perpendicular.

Find boat speed relative to ground.

Answer

[
13m/s
]

(using Pythagoras)

Previous Year JEE & NEET Concept Areas

Although the numerical values differ each year, questions are commonly based on the following themes:

JEE Main

Relative velocity of trains
Relative velocity in one dimension
Boat and river
Galilean transformation
Lift problems
Pseudo force
Constant velocity frames

JEE Advanced

Relative motion in two dimensions
Vector subtraction
Rotating frames
Fictitious force
Advanced lift problems
Multiple moving particles
Constraint motion involving relative velocity

NEET

Definition of frame of reference
Types of frames
Newton’s First Law
Relative velocity basics
Elevator concepts
Pseudo force definition
Inertial vs non-inertial frame

Common Concept Traps

Trap 1

Confusing speed with velocity.

Always remember that velocity has both magnitude and direction.

Trap 2

Ignoring the sign convention.

Choose one direction as positive before solving any problem.

Trap 3

Applying Newton’s Laws directly in accelerating frames.

Always check whether the frame is inertial.

Trap 4

Using simple addition instead of vector addition.

In two-dimensional problems, use vector methods or the Pythagorean theorem where applicable.

Trap 5

Assuming Earth is perfectly inertial.

For advanced discussions, Earth is only an approximately inertial frame because it rotates and revolves.

One-Page Quick Revision Notes

Definitions

Motion is always relative.
A frame of reference is a coordinate system used to describe motion.

Types

Inertial Frame
Non-Inertial Frame

Inertial Frame

Zero acceleration
Newton’s Laws valid
No pseudo force

Non-Inertial Frame

Accelerating or rotating
Newton’s Laws require pseudo force

Relative Motion

Relative Position
Relative Velocity
Relative Acceleration

Galilean Transformation

Applicable only between inertial frames moving with constant relative velocity.

Pseudo Force

Acts opposite to frame acceleration.

Elevator

Upward acceleration

Weight increases.

Downward acceleration

Weight decreases.

Free fall

Weight becomes zero.

Last-Minute Exam Tips

For JEE Main

Memorize all relative velocity formulas.
Practice train, boat, and elevator numericals.
Understand vector subtraction thoroughly.

For JEE Advanced

Focus on derivations of Galilean transformations.
Practice multi-particle relative motion.
Learn to identify inertial and non-inertial frames quickly.
Master pseudo-force applications in accelerating systems.

For NEET

Revise definitions and concepts daily.
Learn the differences between inertial and non-inertial frames.
Practice simple numerical questions based on relative velocity and elevators.
Remember the pseudo-force formula and apparent weight equations.

Complete Chapter Summary

The Frame of Reference is the foundation of classical mechanics because every measurement of position, velocity, and acceleration depends on the observer’s frame. Motion and rest are relative concepts, and different observers may describe the same event differently. Frames are classified into inertial and non-inertial types. Newton’s laws apply directly only in inertial frames, while non-inertial frames require the introduction of a pseudo force to explain observed motion.

The concepts of relative position, relative velocity, and relative acceleration are essential for solving problems involving trains, boats, rain, airplanes, elevators, and moving particles. Galilean transformations describe how coordinates and velocities change between inertial frames, while acceleration remains invariant. These principles form the basis for many questions in JEE Main, JEE Advanced, and NEET, making a strong conceptual understanding and regular problem practice essential for success.

Frame of Refference? complete Notes for JEE and NEET

What is a Frame of Reference?

Simple Definition

NCERT Definition

JEE Definition

NEET Definition

Why Do We Need a Frame of Reference?

Real-Life Examples of Frame of Refference

Example 1: Passenger Inside a Bus

Example 2: Airplane

Example 3: Earth

Example 4: Cricket Ball

Important Terms Related to Frame of Reference

Observer

Object

Coordinate System

Clock

Components of a Frame of Reference

Position of Origin

Coordinate Axes

Observer

Clock

Characteristics of a Good Frame of Reference

Motion Depends on the Observer

Observer A

Observer B

Can an Object Be Both Moving and at Rest?

Example

Absolute Motion vs Relative Motion

Absolute Motion

Relative Motion

Rest and Motion Are Relative

Rest

Motion

Important Note

Mathematical Representation

Everyday Examples of Relative Motion

Walking Inside a Train

Boat Crossing a River

Escalator

Conveyor Belt

Relative Motion Example Images

Common Misconceptions

Misconception 1

Misconception 2

Misconception 3

JEE & NEET Important Points

For NEET

For JEE Main

For JEE Advanced

Quick Revision

Frame of Refference : Part 2

Types of Frame of Reference

Classification of Frames of Reference

Inertial Frame of Reference

Definition

Understanding the Concept

Characteristics of an Inertial Frame

No Acceleration

Velocity May Be Zero or Constant

Newton’s Laws Are Valid

Objects Behave Naturally

Mathematical Condition

Examples of Inertial Frames

Example 1: Person Standing on the Ground

Example 2: Train Moving with Constant Speed

Example 3: Car on a Straight Highway

Example 4: Spacecraft Moving in Deep Space

Image of Inertial Frame

Newton’s First Law and Inertial Frames

Why Is It Called an Inertial Frame?

Important Observation

Non-Inertial Frame of Reference

Definition

Why Do Newton’s Laws Fail?

Characteristics of a Non-Inertial Frame

Frame Has Acceleration

Newton’s Laws Are Not Directly Applicable

Pseudo Force Appears

Observer Experiences Apparent Motion

[
\boxed{\vec v_{AB}

[
\boxed{\vec a_{AB}

[
\boxed{\vec v_{BG}