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# What is  velocity?

Velocity is defined as:”The rate of displacement of a body is called its velocity.”The velocity tells us not only the speed of a body but also the direction along which the body is moving.Velocity of a body is a vector quantity.It is equal to the displacement of a body in unit time.

## What is the formula for Velocity?

Here d is the displacement of the body moving with velocity v in time t.

## Unit for velocity in physics:

SI unit of velocity is the same as speed i.e.,meter per second.

## Uniform velocity:

“A body has uniform velocity if it covers equal displacement in equal intervals of time however short the interval may be.”In equation( d=v t ) is the average velocity of of a body during time t .It is because the velocity of the body may be changing during the time interval t.However,in many cases the speed and direction of a body does not change .In such a case the body possesses uniform velocity.That is the velocity of a body during any interval of time has the same magnitude and direction.

## Average velocity:

“Average velocity is the total displacement covered in any direction in total interval  of time.”or ratio of total displacement to time is called average velocity.

Given data is:

## Instantaneous velocity:

“If a body covers small displacement in in small interval of time than its velocity will be instantaneous velocity such that Δt is equal to zero.”Where Δt is the small interval of time.Average velocity does not tell us about the motion between two points on the path.The path may be straight or curved and the motion may be steady or variable.For example if a squash ball comes back to its starting after bouncing off the wall several times,its total displacement is zero and so also is its average velocity.In such cases the motion is described by instantaneous velocity.

In order to understand the concept of instantaneous velocity,consider a body moving along a path as shown in figure.

At time t 1 let the body be at point P.Its position is given X1. After a short interval time Δt following the instant t,the body reaches the point Q which is described by the position X2. The displacement of the body during this short time interval is given by:

ΔX = X2-X1

The instantaneous velocity at a point P can be found by making Δt smaller and smaller.In this case ΔX will also become smaller and point Q will approach P.If we continue this process ,letting Q approach P ,thus ,allowing Δt and ΔX to decrease but never disappear completely ,the ratio ΔX/Δt approaches a definite limiting value which is the instantaneous velocity.Although Δt and ΔX become extremely small in this process ,yet their ratio is not necessarily a small quantity.Moreover,while decreasing the displacement vector ,ΔX approaches a limiting direction along the tangent at point P.Using the the mathematical language ,the definition of instantaneous velocity Vins is expressed as:

## What is the Escape velocity of earth?

“The velocity required by a body to escape from the earth’s gravitational field.”It is our daily life experience that  an object projected upward comes back to the ground after rising to a certain height.This is due to the force of gravity acting downward.With increased initial velocity,the object rises to the greater height before coming back.If we go on increasing the initial velocity of the object,a stage comes when it will not return to the ground.It will escape out of the influence of gravity.The initial velocity of an object with which it goes out of the earth’s gravitational field,is known as escape velocity.

The escape velocity corresponds to the initial kinetic energy gained by the body,which carries it to an infinite distance from the surface of earth.

We know that the work done in lifting a body from earth’s surface to an infinite distance is equal to the increase in its potential energy:

Where M and R are the mass and radius of the earth respectively.The body will escape out of the gravitational field if the initial kinetic energy of the body is equal to the increase in potential energy of the body in lifting it up to infinity.Then

## Angular velocity:

“Time rate of change of angular displacement is known as angular velocity.”It is denoted by ω,its formula is given by:

Unit of angular velocity is radian per second (rad s-1) .

Very often we are interested in knowing how fast or how slow a body is rotating.It is determined by its angular velocity which is defined as the rate at which the angular displacement is changing with time.If Δθ is the angular displacement during the time interval Δt ,the average angular velocity ωav during this interval is given by:

The instantaneous angular velocity ω is the limit of the ratio Δθ/Δt as Δt ,following instant t,approaches to zero.

Thus:

In the limit when Δt approaches zero,the angular displacement would be infinitesimally small.So it would be a vector quantity.Its direction is along the axis of rotation and given by right hand rule.

## Types of angular velocity:

### Average angular velocity:

“Total rate of change of angular displacement is called average angular velocity.”

### Uniform angular velocity:

“If rate of change of angular displacement is constant is called uniform angular velocity.”

### Non uniform angular velocity:

“If rate of change of angular displacement is not constant is called non uniform angular velocity.”

### Instantaneously angular velocity:

“Angular velocity at particular instant of time is called instantaneous angular velocity.”

## Relationship between power and velocity:

It is some times,convenient to express power in terms of a constant force F acting on an object moving at constant velocity v.For example,when the propeller of a motor boat causes the water to exert a constant force F on the boat,it moves with a constant velocity V.The power delivered by the motor at any instant is given by:

The dot product of force and velocity is called power.

See also terminal velocity:

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