## What Is Relative Motion

The concept of reference frames was first introduced to discuss relative motion in one or more dimensions. When we say an object has a certain velocity, then this velocity is with respect to some frame that is known as the reference frame. In everyday life, when we measure the velocity of an object, the reference frame is taken to be the ground or the earth.

For example, if you are travelling in a train and the train is moving at a speed of 100 km/hr, then your speed according to another passenger sitting on that train is zero. According to him, you are not moving. But if someone observes you from outside the train, standing on the ground, according to him, you are moving with 100 km/hr as you are on the train and the train is moving with 100 km/hr.

Here, the motion observed by the observer depends on the location of the observer. This type of motion is called relative motion.

## How To Find Relative Velocity In Physics

The relative velocity of body A with respect to body B is given by

The relative velocity of body B with respect to body A is given by

Here, is the angle between and

For two bodies moving in the same direction magnitude of relative velocity is equal to the difference in magnitudes of their velocities.

For two bodies moving in opposite directions magnitude of relative velocity is equal to the sum of the magnitudes of their velocities.

## Relative Motion In Physics

Relative motion in Physics is a vital concept that students must master. In this article, we will learn what relative velocity is and how to use this concept to solve real-life physics problems.

Let us consider two cars, A & B moving in the same direction on the road with equal speed.

To a person seated in car A, if he were unconscious of his motion, car B would appear to be at rest. The line joining the two cars will always remain constant in magnitude and direction. The velocity of B relative to A or the velocity of A relative to B is zero.

On the other hand, if A is moving at 30 km/hr and B at 40 km/hr in the same direction, B appears to be moving away from A at a rate of 10 km/hr. This represents the velocity of B relative to A.

If, however, B is moving opposite to the direction of A with a velocity of 40 km/hr, for a person in A, B appears to draw away from him at a rate of 70 km/hr. This represents the velocity of b relative to A.

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## Train Passenger And Observer

Now let us consider the train to be stationary in the platform and an observer to be on the platform sitting on the bench.

**When the train slowly starts to move the observer appears to be in motion to the passenger on the train. Basically here the frame of reference concepts dives in, that is, the frame of reference of the passenger on the train is said to be stationary relative to the frame of reference of the observer on the platform.**

The passenger on the train in motion observes the observer on the platform to be in motion because the motion of the train is in the direction opposite to that of the observer on the platform. In such cases both the observer and the passenger appears to be in relative to each other.

## Definition Of Relative Velocity

When the distance between two moving points A and B are changing, either in magnitude or in direction, or both, each point is said to possess a velocity relative to the other.

The velocity of one of the moving points say A relative to other point B is obtained by calculating with the velocity of A, the reversed velocity of B. The velocity of A relative to B is the velocity with which A will appear to move to B, if B is reduced to rest. If velocity of body A is and that of B is with respect to stationary frame, then from the definition, relative velocity of A with respect to B, is given by

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## Why Is Rest And Motion Relative

Rest and motion are the relative terms because they depend on the observers frame of reference.If an observer is at rest in his or her own frame of reference,but he may be moving in other observers frame of reference.

**George Jackson** is the founder and lead contributor of Physics Network, a popular blog dedicated to exploring the fascinating world of physics. George has always been passionate about physics and its ability to explain the fundamental workings of the universe. He received his Ph.D. in physics from the University of California, Berkeley, where he conducted research on particle physics and cosmology. After completing his degree, George worked as a postdoctoral researcher at CERN, the world’s largest particle physics laboratory. It was there that he first had the idea to create a resource for physics enthusiasts of all levels to learn about and discuss the latest developments in the field. When he’s not busy exploring the mysteries of the universe, George enjoys hiking and spending time with his family.

## What Is Relative Velocity Explain With An Example Class 8

Definition of relative velocity. : the vector difference between thevelocities of two bodies : the velocityof a body with respect to another regarded as being at rest comparerelative motion. For example, you can toss and catch a ball in a moving bus if themotion is in a straight line at constant speed.

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## Is The Ap Physics C Exam Hard

AP Physics C E/M is rated as very hard to self-study relative to other AP classes, and AP Physics C Mechanics is rated as quite hard to self-study. A survey of AP alumnae asked for a rating out of 10 for how easy each class is to self study, with 1 = easiest to self study, 10 = hardest to self study. What is this?

## The Frame Of Reference And Its Importance In Relative Motion In Physics

A frame of reference is a coordinate system plus a time scale. It calculates the positions, velocities, and accelerations of bodies or objects in that frame.

Different frames of reference may move relative to one another.

A frame of reference is particularly important when describing an objects displacement, velocity, and acceleration. Displacement is the change in the position of an object relative to the frame of reference. The frame can be chosen according to the convenience of the situation. The position **r**, velocity **V** and the acceleration **a** of particle depend on the frame of reference. We can relate the position, velocity, and acceleration of a particle measured in two different frames of reference. With the help of a frame of reference, we can analyze relative motion in one dimension, river-boat problem, rain, man problem, and describe the motion of a plane in a storm.

Using a good frame of reference can reduce the problems based on relative motion in Physics very easy to solve.

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## Why All Motion Is Relative

Explain the statement All motion are relative. The motion of an object with respect to another object is nothing but relative motion. For example, if you are traveling on a train then you are at rest with respect to the observer on the train, but you are in motion with respect to the person outside the train.

## Who Proposed The Concept All Motion Is Relative

Galileo was the first to point out the obvious: all motion is relative. When I say something like the ball is traveling at 50 mph towards me, I implicitly add relative to my head. If Im on a train, someone standing on the platform would add the speed of the train to the speed of the ball to get the total speed.

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## Park Location To An Observer

Let us a simple play to explain this better. The children were allowed to play in the evening in the park but the location of the park was unknown, so the caretaker inquires the park location to the local person.

**The local person knows the direction and says that the park is located to their north but before that they will have to cross the signal. So now let us go detailed about this.**

The entire group moves **north direction** and after crossing the signal they end up at the park. But also there are other group of children coming to the park form the south direction where they will reach the park without having to cross the signal.

There will be a motion which is relative to both the **group of children coming to the park**. For the group moving north the park appear on the left and for the group moving south will find the park to their right. So both the group is said be in relative motion to one other.

## The Velocity Of Relative Motion In One Dimension:

Objects can only move in one of two directions: either in the same direction or in the opposite direction. The objects are moving in a one-dimensional manner, with positive velocity, to produce relative motion. An example of this is if a person is sitting inside a moving train and the train is moving in the direction of the reference frame . With this type of example, the value of velocity with respect to the earth can be written as vTE = 10 m/s, where TE stands for the train. The relative velocity is the speed at which the train is moving relative to a stationary person inside the train. Due to the direction of motion of the person, the relative velocity of the person with respect to the reference frame of the train is vPT = -2 m/s, where vPT is the relative velocity of the moving person inside the train. With respect to the reference frame of earth, the above two relative velocity factors can be added together to determine the total relative velocity.

VPE = VPT + VTE

Through the equation above, we can easily determine the total relative velocity of the train and the individual relative to the reference frame of earth.

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## The Motion Of A Boat In A River

Boat motion is classified into three categories based on the angle between VBR and VR.

Velocity of the boat with respect to the river

Velocity of the river with respect to the ground.

#### Down stream

Resultant velocity of the boat

The time taken for the boat to move a distance d along the direction of flow of water is

#### Up stream

Resultant velocity of boat

The time taken for the boat to move a distance d opposite to the direction of flow of water is

#### General approach :

Let the boat starts at point A on one bank with velocity and reach the other bank at point D.

The component of the velocity of the boat antiparallel to the flow of water is .

The component of velocity of a boat perpendicular to the flow of water is .

So, the time taken by the boat to cross the river is .

Along with the flow of water, the distance traveled by boat or the drift is

Or, BD = drift distance

The boat will reach the other end of the river to the right of B if .

The boat will reach the other end of the river to the left of point B if .

The boat reaches the exactly opposite point on the bank if .

#### The motion of the boat crossing the river in the shortest time :

The time taken by boat to cross the river will be minimum if .

Where d is the width of the river.

This time is independent of the velocity of river flow.

Velocity of boat with respect to the ground has magnitude, .

The direction of resultant velocity is.

#### Motion of a boat crossing the river in shortest distance :

This will be possible only when .

## Who Discovered Relative Motion

Galileo was the first to point out the obvious: all motion is relative. When I say something like the ball is traveling at 50 mph towards me, I implicitly add relative to my head. If Im on a train, someone standing on the platform would add the speed of the train to the speed of the ball to get the total speed.

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## Relative Motion In One And Two Dimensions

- Explain the concept of reference frames.
- Write the position and velocity vector equations for relative motion.
- Draw the position and velocity vectors for relative motion.
- Analyze one-dimensional and two-dimensional relative motion problems using the position and velocity vector equations.

Motion does not happen in isolation. If youâre riding in a train moving at 10 m/s east, this velocity is measured relative to the ground on which youâre traveling. However, if another train passes you at 15 m/s east, your velocity relative to this other train is different from your velocity relative to the ground. Your velocity relative to the other train is 5 m/s west. To explore this idea further, we first need to establish some terminology.

## What Is Relative Motion And Rest

Rest and motion are the relative terms because they depend on the observers frame of reference.If an observer is at rest in his or her own frame of reference,but he may be moving in other observers frame of reference.

**George Jackson** is the founder and lead contributor of Physics Network, a popular blog dedicated to exploring the fascinating world of physics. George has always been passionate about physics and its ability to explain the fundamental workings of the universe. He received his Ph.D. in physics from the University of California, Berkeley, where he conducted research on particle physics and cosmology. After completing his degree, George worked as a postdoctoral researcher at CERN, the world’s largest particle physics laboratory. It was there that he first had the idea to create a resource for physics enthusiasts of all levels to learn about and discuss the latest developments in the field. When he’s not busy exploring the mysteries of the universe, George enjoys hiking and spending time with his family.

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## What Is Relative Motion And Why Is It Important

The concept of relative motion refers to the comparison of two rigid bodies relative accelerations and velocities. It is easy to say that the motion of any two objects can be compared as relative motion. The relative motion of an object with respect to another object is known as its reference frame.

## What Is The Use Of Relative Velocity

We can use the relative velocity of one car relative to the other to find how long it would take for the faster car to catch up to the slower car. In order to work out the velocity of one car relative to another, we need to subtract the velocity of the car we are observing from the velocity of the other car.

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## Relative Motion Analysis: Position Velocity And Acceleration

Consider two frame of references and and suppose a particle P is observed by both frame of references. The frames may be moving with respect to each other

The position vector of particle P with respect to frame is . This position vector of the particle with respect to frame is

Differentiating equation with respect to time again,

*Equation is known as the equation of relative position.*

*Equation is known as the equation of relative velocity.*

*And Equation is known as the equation of relative acceleration.*

is the velocity of the particle with respect to ,

is the velocity of particle with respect to frame and

is the velocity of frame with respect to frame

## How Do We Solve The Relative Motion Of The Objects That Are In Two Dimension

First, we must establish the reference frame common to both vehicles, which is Earth. Then, we write the velocities of each with respect to the reference frame of Earth, which enables us to form a vector equation that links the car, the truck, and Earth to solve for the velocity of the car with respect to the truck.

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## Relative Velocity In Two Dimensions

We can now apply these concepts to describing motion in two dimensions. Consider a particle *P* and reference frames *S* and ^, as shown in . The position of the origin of ^ as measured in *S* is }_^S}, the position of *P* as measured in ^ is }_^}, and the position of *P* as measured in *S* is }_.

**Figure 4.26** The positions of particle P relative to frames S and ^ are }_ and }_^}, respectively.

From we see that

The relative velocities are the time derivatives of the position vectors. Therefore,

*The velocity of a particle relative to S is equal to its velocity relative to* ^ *plus the velocity of* ^ *relative to S*.

We can extend to any number of reference frames. For particle *P* with velocities }_,}_\text\,\text\,}_ in frames *A*, *B*, and *C*,

We can also see how the accelerations are related as observed in two reference frames by differentiating :

We see that if the velocity of ^ relative to *S* is a constant, then }_^S}=0 and

This says the acceleration of a particle is the same as measured by two observers moving at a constant velocity relative to each other.

## Relative Motion In Two Dimensions

The same concept will be applicable in two-dimensional motion. If you have to find the velocity of A with respect to B, assume that B is at rest and give the velocity of B to A in the opposite direction.

Let us consider two objects A and B which are moving with velocities Va and Vb with respect to some common frame of reference, say, with respect to the ground or the earth. We have to find the velocity of A with respect to B, so assume that B is at rest and give the velocity of B to A in the opposite direction.

Vab = va vb

Similarly, for the velocity of object B with respect to A, assume that A is at rest and give the velocity of A to B in the opposite direction.

Vba = vb va

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