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What is Velocity? Definition, SI Unit, Examples & Applications

Hello everyone! I hope this article will find you in great health. Today, in this article, we will discuss in detail: What is velocity? We will take a look at what exactly velocity is, how it can be measured, what scale has System International (SI) defined to measure the velocity, how many forms of velocity do exist in our surroundings, and what are the real-life applications of this physical quantity?

I will let you guys know about how velocity is a regular part of our daily lives and how it behaves in the environment we are living in. To understand the basic concept we need to have a deeper look at its real-life examples. A detailed discussion on velocity to have a better understanding is provided in the next section. Let’s get started.

What is Velocity?

An earthly object can possibly have two states i.e. rest or motion. If an object is in motion, a numerical value called Speed is used to measure how fast or slow the object is moving? Speed is defined as the distance covered per unit of time. So, if an object covers a distance of 1 meter in 1 second, its speed will be 1m/s. As speed is a scalar quantity so it just gives the scalar information(about motion) and doesn't tell us anything about the direction of the movement i.e. object is moving towards north, south or may have a circular motion.

So, in order to completely define the motion of an object, an equivalent vector quantity of speed was introduced and named Velocity. Velocity, not only gives the numerical value(speed) but also tells the direction of the moving object. In simple words, speed plus direction is equal to velocity and as speed is distance per unit time, similarly velocity is displacement per unit time.

Now let's have a look at a proper definition of Velocity:

Velocity Definition

• The velocity of an object is defined as the displacement(covered by it) per unit time in a particular direction.
• If two objects are moving in the same direction at different speeds OR in different directions at the same speed, they will have different velocities.
• Two objects will have the same velocities, only if both are moving in the same direction with the same speed.

Let's have a look at the symbol of velocity:

Velocity Symbol

• Symbols are used to represent physical quantities as writing the full name is time-consuming and sometimes overwhelming.
• The symbol used to represent Velocity is "v"(small character).
• As it's a vector quantity, so its symbol is either written in bold or with an arrowhead at the top.
• Sometimes, v(t) is also used as a velocity symbol, where t shows the time span.
• The below figure shows the velocity symbol more clearly:

Now let's have a look at the mathematical formula for calculating the velocity of an object:

Velocity Formula

• Velocity is defined as displacement per unit time, so its formula is:

Velocity = Displacement / Time

v = d/t

As v & d are both vector quantities, so written in bold while t is a scalar quantity.

• If we are calculating the average velocity of an object, the velocity formula will be:

Average Velocity = Distance Covered / Total Time

?v = ?d/?t

?v = (d2 - d1) / (t2 - t1)

where t1 & t2 are initial and final time intervals and d1 and d2 are initial and final displacements of the object.

Now, let's drive the velocity unit from its formula:

Velocity Unit (SI)

• As Velocity formula is:

Velocity = Displacement / Time

where SI unit of displacement is the meter and that of time in seconds.

• So, the SI unit of velocity is:

Velocity = meter / second

• SI unit of velocity is normally written as m/s or ms^-1.
• Other velocity units are:
  1. ft/s
  2. mph
  3. km/h etc.

In the game of cricket, the velocity of the ball is usually not measured in SI units rather they measure it in either kilometer per hour or miles per hour.

Velocity Dimensions

• Since the unit of displacement(meter) shows the quantity of length so its dimension would be “L”.
• Similarly, when it comes to the “second” it shows the amount of time so its dimension will be “T”.
• Putting these dimensions in the velocity formula, we have.

Velocity Dimension = [L/T]

v = [LT^-1]

 

Few Velocity Terms

Depending upon various factors, velocity has been divided into multiple types as discussed below. Let’s read through them all.

Negative Velocity

• If an object is moving in a coordinated plane, then its velocity is measured from some fixed reference point.
• In such cases, if the object is moving away from the reference point, its velocity is termed as Negative Velocity.

Let's understand it with an example of a ball thrown upwards:

As we know, Earth's gravitational force pulls everything towards it. So, considering the earth as a reference point, when you throw a ball in the upward direction, it's moving away from its reference point(Earth's center). So, during its upward flight, the ball will have a negative velocity and thus is written with a negative sign.

Zero Velocity

• When an object is not covering any distance with respect to the varying time, it will be said to have Zero Velocity.

Let's continue that example of the ball moving upward:

As we have seen in the previous section, the ball will have a negative velocity while moving upward. But when it will reach the maximum height and rite before moving back in the downward direction, for an instance it will have a zero velocity, as it won't be moving either upward or downward.

Positive Velocity

• If the object is moving towards the reference point of its coordinate system, its velocity is termed as Positive Velocity.

Let's add some more in that ball example:

Once the ball reaches the maximum height, it will start moving back in the downward direction. Now, the ball is moving towards its reference point(Earth's Core) so it will be said to have positive velocity now.

Initial Velocity

• As moving objects have variable velocities over different periods of time, that's why velocity is normally measured in the rate of change(?v).
• So, the first velocity of the object, when it comes under observation is termed as Initial Velocity.
• The Initial Velocity is also termed as the velocity of an object at time t = 0.
• Initial velocity is denoted in Physics by the alphabetic letter "u" or "Vi".

Let's understand it with the same example:

We have seen the ball example thrown upward. If we consider both of its loops(moving upward and then downward), its initial velocity will be right where it left the hand of the thrower. It will have a maximum initial velocity as during the upward direction it will slow down and during the downward direction, it will lose some to friction. But if we only consider the second loop i.e. the ball has reached its maximum position and now it's moving downwards. So, in this scenario, the initial velocity of the ball will be 0. I hope it got cleared.

Initial Velocity Formulas:

• Using the equation of motion, we can easily derive different mathematical expressions for the initial velocity. The first equation of motion is,

v = u + at

• If we are provided with the time, final velocity, and acceleration, we can calculate the initial velocity using the formula given below.

u = v - at

The above expression shows when we multiply acceleration with the given time and subtract this product from the final velocity, it gives us the initial velocity.

• If a scenario comes where distance, final velocity, and acceleration are provided, we can find initial velocity from a mathematical expression given below:

u² = v² - 2aS

• In case, we have only time, distance and acceleration to find out the initial velocity, we can use the formula shown below.

u = S/t - (1/2) at

• If the final velocity, time, and distance are provided in the statement, an effective way to find out the initial velocity is given below.

u = 2(S/t) - v

 

where,

• u = initial velocity.
• v = final velocity.
• a = acceleration.
• t = time consumed.
• S = distance covered.

Final Velocity

• The velocity of a body at the end of the provided time is known as the Final Velocity.
• We can also define Final Velocity as the last velocity of the object while it's under consideration.
• The final velocity is usually denoted by “v” or “V_f”.

Final Velocity Formulas

• Using the equation of motion, the final velocity can be easily calculated with the formula given below, when we are provided with the initial velocity, acceleration, and time consumed:

v = u + at

or

V_f = V_i + at

• If the statement has asked us to calculate the final velocity and provided us with distance, initial velocity, and acceleration. We can use the below formula for quick calculations.

V_f² = V_i² + 2aS

Where,

• V_f = Final Velocity.
• V_i = Initial Velocity.
• S = Distance covered.

Let's understand the concept associated with the final velocity through a visual example.

A projectile motion of the ball thrown from one end is shown in the figure below. At time zero (t = 0), when a guy in a purple shirt throws a ball, the velocity of that ball at this time is considered initial velocity. After reaching a particular height, when the ball starts moving downwards and reaches at t = 8 seconds in the hands of a guy wearing a green shirt. At t = 8 seconds, the velocity of the ball is the final velocity. After this velocity, an object comes again into the stationary position.

Similarly, if you drop a ball from a specific height and allow it to move towards the ground as shown in the figure below. The moment you drop the ball, the velocity is called initial velocity. Whereas, the moment when the ball touches the ground, the velocity will be known as the final velocity.

Now let's have a look at different types of velocity in detail:

Types of Velocity

Depending on the type of object and its motion, we have numerous types of velocities, a few of them as discussed as follows:

Average Velocity

• When an object is moving in a specific direction, the ratio between the total displacement covered and total time consumed is known as the average velocity of that particular body in motion.
• It is denoted by “v” or "Vav".
• We can also define this quantity as the average rate at which the body changes its position from one point to another point.

Average velocity = total displacement covered / total time taken

• If we take the difference between the initial and final displacements and divide it by the difference of initial and final time, it will give us average velocity in return.

?v=?x/?t

?v = (x2-x1) / (t2-t1)

Where,

• x2=final displacement
• x1=initial displacement
• t2=final time
• t1=initial time

Average velocity cannot tell us how fast or slow an object is moving in a specific interval of time and for that, we have another type of velocity called Instantaneous velocity.

Instantaneous Velocity

• The velocity of an object at a particular instant is known as the instantaneous velocity of that object.
• In other words, the velocity of a moving body at a specific point is its instantaneous velocity at that point.
• Instantaneous velocity is similar to average velocity but we need to narrow the time intervals i.e. time approaches to 0.
• It is denoted by “Vinst”.
• If any subject has a fixed velocity over a specific time period then its instantaneous and average velocity will be the same.

By applying a limit “t” approaches zero on the average velocity provides us with the instantaneous velocity as shown in the formula given below.

V_inst = Lim _{t -> 0} (?d/?t)

Take a look at the figure below, the velocity at point “p” depicts the instantaneous velocity of a moving body.

The figure below shows the relation between average and instantaneous velocity. The velocity is represented by the red line and has been divided into several segments. The position is displayed on the y-axis whereas the x-axis shows the time consumed. In the first interval, Jack has covered 3 miles in the first 6 minutes. In the second interval, Jack stopped for 9 minutes. Whereas, in the third interval, Jack covered another 5 miles in 15 minutes. If we divide the total displacement covered by Jack by the total time consumed during the whole travel, it will give us an average velocity.

Constant Velocity

• If a body is traveling at the same speed for a long time and is not changing direction, then its velocity will be considered as Constant Velocity for that particular interval of time.
• In other words, it can be said that a body will have a constant velocity if it is moving at a constant speed along the straight line. This straight line can be represented by the formula given below.

x=xo+vt

Where,

xo=position of the body at t=0

• An object can have a constant velocity if it is moving in the presence of very little or no friction. Less friction allows that object to move freely just like in ice hockey where a hockey puck slides on the ice as shown in the figure below.
• If an object is moving with a constant velocity, it will have zero acceleration because acceleration is the rate of change of velocity per unit time.

a=dv/dt=0 v=constant

This scenario can be visualized through a velocity-time graph as shown in the figure below. You can see a straight line for each time interval depicting the velocity is constant throughout with “0” acceleration.

Variable Velocity

• If the velocity of an object is changing in either direction or magnitude or both, it is said to have a Variable Velocity.
• If an object is in a motion and is covering unequal distances for every equal interval of time, we can say it is moving with a variable velocity.
• In simple words, variable velocity is a type of velocity that changes with time.

Let's understand this from a real-life example.

For instance, if a fan installed in your room is rotating at a continuous speed, its velocity will be variable because its direction gets changed every time.

Orbital Velocity

• The velocity required to make an object overcome its gravitational force and rotate within an orbit is called orbital velocity.
• The movement of satellites around the earth and the movement of stars around the sun are the best examples of orbital velocity.
• It is denoted by “Vorbit” and for Earth, its mathematical formula is:

Vorbit=GMR

Where,

• G=gravitational constant=6.6710-11m3kg-1s-2
• M= mass of the planet
• R=radius

Escape Velocity

• Escape velocity is the type of minimum velocity required for an object to escape from the gravitational force of a massive body (moon, earth, etc.) and to move out somewhere in space.
• Escape velocity increases with an increase in the mass of a body.
• It is denoted by “ve” and depends upon various parameters including the mass of the planet and radius.
• We can calculate it using the mathematical expression given below.

ve=2GMr

Where,

• G=gravitational constant.
• M=mass of the planet.
• r=radius.

Angular Velocity

• The rate of velocity at which a body rotates around a particular point or center in a given amount of time is called angular velocity.
• It can also be defined as the angular speed at which a body rotates along a specific direction.
• Angular velocity is denoted by omega “?”.

Angular Velocity Unit

• System International has assigned this quantity with a unit known as radians per second.
• This quantity can also be measured in many other units as well depending on the requirements and they include:
  1. degrees per second
  2. degrees per hour

Let's have a look at how to find the angular velocity of a moving object?

Angular Velocity Formula

To calculate this quantity, a formula is given below.

?=??/?t

Or,

?=v/r

Where,

• v=linear velocity
• r=radius
• ?=angular velocity

Conversion of Angular Velocity into Rotational Velocity

• When we measure angular velocity in either revolution per minute or rotations per unit time, it becomes rotational velocity.

The direction of motion of an object moving with angular velocity is always perpendicular to a plane of rotation. It can be measured using the right-hand rule. The whole concept is shown in the figure below.

 

Linear Velocity

• As it is very clear from the name of this quantity, when an object moves along a straight line in a single direction, its velocity will be a linear velocity.
• It is simply denoted by the alphabetic letter “v”.

The above figure shows that the linear velocity is dependent on the two different parameters i.e., distance covered and the time consumed to cover that particular distance.

Let's have a look at how to find linear velocity?

Linear Velocity Formula

It can be calculated using the below mathematical expression.

velocity=distance/time

v=S/t

As we know,

S=r?

Putting this value in the above formula we have,

v=r?/t

The linear velocity can also be represented in terms of an angular velocity as given below.

v=r?

Terminal Velocity

• A steady speed that an object achieves when falling through the liquid or gas is known as its terminal velocity.
• In other words, we can describe this quantity as the constant vertical velocity of an object.
• It can also be defined as the highest velocity maintained by a body that is falling through the liquid
• It is denoted in Physics by “vt”.

Factors Involved in Terminal Velocity

• This quantity is dependent on multiple factors e.g.,
  1. the mass of the object
  2. drag coefficient, acceleration
  3. projected area
  4. fluid density.

Terminal Velocity Formula

• Terminal velocity can be calculated using a mathematical expression given below:

vt=2mgACd

Where,

• vt=terminal velocity
• g=gravitational acceleration=9.8 ms-2
• m=falling object's mass
• Cd=drag coefficient
• A=projected area
• ?=fluid density

Uniform Velocity

• A scenario when a moving body is covering the equal displacement in equal internal in a fixed direction is said to have a uniform velocity.
• It is a stable velocity that does not change in multiple intervals of the time consumed and direction remains the same too.

Let's understand with an example.

• A motorbike traveling with a speed of 20 kilometers per hour towards the east has uniform velocity.
• Uniform velocity can be easily visualized on the distance-time graph as shown in the figure below.

Non Uniform Velocity

• A body that covers unequal displacement in equal time intervals is said to have non-uniform velocity.
• In this case, either direction of motion or both rate of motion and direction can be changed for an object in motion.

Let's understand this with a visual example.

The track of a car moving with non-uniform velocity is shown in the below figure. Unequal displacements covered in equal intervals of time can clearly be seen from the velocity-time graph.

Relative Velocity

• Relative velocity is the vector difference between the velocities of two different objects.
• It can also be defined as the velocity of an object with respect to an observer who is at rest.

Let's understand the overall scenario with an example.

For instance, the air is causing some hindrance in the airplane’s track or a boat is traveling through the river whose water is flowing at a particular rate. In such cases, to observe the complete motion of the object, we need to consider the effect of the medium affecting the motion of a moving body. By doing so, we measure the relative velocity of that moving object as well as the medium’s velocity affecting its motion

Let's have a look at another example to have a better understanding of relative velocity.

Finding Relative Velocity

• The relative velocity of an object “x” relative to the object “y” can be expressed as shown below.

Vxy=Vx-Vy

• Similarly, the relative velocity of an object “y” relative to the object “x” is given below.

Vyx=Vy-Vx

• Taking a look at the above equations, we can develop it as:

Vxy=-Vyx

• The above equation shows that both relative velocities are equal in magnitude but opposite in direction.

|Vxy|=|Vyx|

• In the first case, the observer is moving in the rightwards and the ball was thrown by a girl is moving in the same direction and the person dragging that girl is traveling in the same direction as well. Therefore, all these quantities are positive.
• In the second case, the girl is throwing the ball in opposite direction to the direction in which the observer is moving. That is why the signs of the velocities are negative for both the observer as well as the ball.

Now, let's have a look at what parameters creates a difference between speed and velocity.

Difference Between Velocity and Speed

It has been proved through various research studies that most of the time people get confused when it comes to speed and velocity. They mostly get confused in implementing their concepts separately in different scenarios as and when needed.

Basic Difference

If I tell you the very basic difference between these two quantities, they are just as different as distance and displacements are.

• Speed is the rate of change of distance with respect to the time consumed in covering that particular distance.
• Whereas, velocity is the rate of change of displacement (shortest distance) covered by a moving object in a specific direction per unit of time.

Let's have a look at some more points to understand the difference effectively.

• Speed depicts that how fast an object has the ability to move. An object at a stationary position always has zero speed. The speed needs no direction to be defined.
• It is a necessity for someone to consider the direction in which a body is moving if one is going to describe the velocity.

Therefore, keeping in mind the above points, it can be said that a direction creates a major difference between speed and velocity.

• The quantity that doesn’t require direction to be measured is known as the scalar quantity and it only needs magnitude to be defined. Therefore, speed falls into the category of scalar quantities.
• The quantities that need direction and cannot be defined without it are known as the vector quantities. Therefore, velocity belongs to the family of vector quantities.

Let's understand through an example.

For instance, 30 kilometers per hour is the speed of a moving vehicle whereas 30 kilometers per hour east shows the velocity of the same vehicle.

• It is very simple to calculate the speed of any moving object compared to calculating the velocity of the same object.
• Average speed is the ratio between distance traveled and the time taken.
• Whereas, the average velocity is the ratio between the change in position (?S) and the change in time (?t) consumed.

Findings

• In the light of the above discussion, we can say that the speed with the direction forms a velocity.
• In order to provide a much better understanding of speed and velocity and their basic differences are listed in the table shown below.

Parameters	Speed	Velocity
Definition	The rate at which a body covers a particular distance is commonly known as speed.	The rate at which a body changes its position in a specific direction is called velocity.
Magnitude	Speed is always positive and it cannot be either negative or zero.	Velocity can be positive, zero, and negative depending upon the direction in which an object is moving.
Quantity Type	Speed does not need any direction for its description so, it is a scalar quantity.	Velocity cannot be described without direction so it is a vector quantity.
Change in Direction	Change in direction does not matter when calculating average speed.	Every change in direction changes the velocity.
Formula	s=distancetime=dt	s=change in positionchange in time=st
SI Units	Meter per second (m/s)	Meter per second (m/s)

Examples of Velocity

A few examples of velocity from real-life are presented to clear your concepts related to it if there still exists any confusion.

• Suppose, you go to your school to maintain your studies on a daily basis. The school is situated to the west of your home. Here, you can observe that you always go towards the west from the starting point which means you go in a particular direction that depicts velocity. Your speed could be high or low.
• In the game of cricket, when a ball is thrown by the baller towards a batsman is also a great example of velocity from our daily life because it follows a single direction.
• The way the moon revolves around the earth and the earth moves around the sun is another example of velocity from nature because of its single direction.
• The ceiling fan rotating in your home during summers also belongs to the family of velocity due to its either clockwise or anti-clockwise rotation.
• The movement of the train from one city to another also follows a specific track in a single direction.
• A revolution of a launched satellite around the earth.
• Water coming from the tap when you open it.
• The flow of the river (it depicts variable velocity).
• Anyone doing morning walk or running.

Final Words

This is all from today’s article. I have tried my level best to explain to you each and everything associated with the velocity. I have focused in detail on its basic concept, various forms, unit assigned by System International, and visual examples where needed. Moreover, I have provided you with a couple of examples captured from real life so that you can have a better understanding of velocity.

I hope you have enjoyed the content and are well aware of this topic now. If you are looking for more similar information, stay tuned because I have a lot more to share with you guys in the upcoming days. In case you have any concerns, you can ask me in the comments. I will surely try to help you out as much as I can. For now, I am signing off. Take good care of yourself and stay blessed always.

Thank You!