## Finding The Angular Velocity Direction

The angular velocity direction is difficult to track because a point on a rotating object constantly changes direction. The axis of the rotating object is the only point where the object has a fixed direction. With the help of the axis of rotation, the direction of angular velocity is determined by the Right Hand Rule.

## Difference Between Speed And Velocity

The basic difference between speed and velocity is that the former has only magnitude, while velocity has both magnitude and direction. It means the velocity is the speed with direction.

Other Detailed Differences between Speed and Velocity are as Follows:

Speed is the quantitative measure of how fast a body is moving, whereas velocity measures not just the speed at which the body is moving but also the direction in which it is moving. In other words, speed determines only how fast something is travelling, while velocity determines how fast something is travelling, along with the direction of its movement.

As the speed emphasizes only the magnitude, it is termed as a scalar quantity. On the other hand, the velocity is a vector quantity as it focuses on both the magnitude and direction.

Speed is defined as the rate of change of distance, whereas velocity refers to the rate of change of displacement.

The average speed of a moving body can never be zero or negative. But, the velocity of a moving body can undoubtedly be zero.

Speed is distance/ unit time. On the other side, velocity is displacement/ unit time.

## Velocity And Acceleration In A Pendulum

When a pendulum swings from side to side, its velocity and acceleration vary both in magnitude and in direction at each point during the motion.

The magnitude of **velocity** of a pendulum is highest in the center and lowest at the edges. On the other hand, the magnitude of its **acceleration** is highest at the edges and lowest at the center.

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## International Prototype Metre Bar

The influence of the intellect transcends mountains and leaps across oceans. At the time when warned his fellow countrymen against entangling political alliances with European countries, there was started a movement of far reaching importance in a small country in the heart of the Alps which exerted a silent, yet potent scientific influence upon the young republic on the eastern shores of North America.

In 1816, was appointed first Superintendent of the . Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for in the United States.

Since 1830, Hassler was also head of the Bureau of Weights and Measures which became a part of the Coast Survey. He compared various units of length used in the United States at that time and measured to assess temperature effects on the measurements.

In 1864, refused to join the first general conference of the because the French geodetic works had to be verified.

Hassler’s metrological and geodetic work also had a favourable response in Russia. In 1869, the sent to the a report drafted by , and inviting his French counterpart to undertake joint action to ensure the universal use of the in all scientific work.

## Other Units Incorporating Seconds

A second is directly part of other units, such as measured in , in meters per second, and in meters per second squared. The metric system unit , a measure of radioactive decay, is measured in inverse seconds. Though many derivative units for everyday things are reported in terms of larger units of time, not seconds, they are ultimately defined in terms of the SI second this includes time expressed in hours and minutes, velocity of a car in kilometers per hour or miles per hour, kilowatt hours of electricity usage, and speed of a turntable in rotations per minute.

Moreover, most other are defined by their relationship to the second: the is defined by setting the to be 299 792 458 m/s, exactly definitions of the SI base units , , , and also depend on the second. The only base unit whose definition does not depend on the second is the , and only two of the 22 named derived units, and , do not depend on the second either.

A set of atomic clocks throughout the world keeps time by consensus: the clocks “vote” on the correct time, and all voting clocks are steered to agree with the consensus, which is called . TAI “ticks” atomic seconds.:207218

Civil time is defined to agree with the rotation of the Earth. The international standard for timekeeping is . This time scale “ticks” the same atomic seconds as TAI, but inserts or omits as necessary to correct for variations in the rate of rotation of the Earth.:1617,207

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## The Formula Of Velocity In Physics For Class 9

Velocity is the rate of change in displacement with respect to time i.e. it is a measurement of how long it takes an object to travel in a straight line to its destination. Velocity is a two-dimensional vector quantity with magnitude and direction, which means velocity has magnitude and direction. The unit of velocity is meter per second and it is represented by V. If students are still confused about what velocity is then we have simplified it more, check the definition given below we have compared the distance with displacement to clear the confusion of student.

It relates to the rate at which displacement changes over time. Furthermore, the velocity is defined by distance and displacement. There will also be no velocity if there is no displacement in the objects potion and the object does not travel any distance. So, what exactly is the distinction between displacement and distance? The net change in the position of a moving object is referred to as displacement. Distance, on the other hand, refers to the amount of ground covered by a moving item.

## Velocity Formula Physics For Class 9 11

Lets have a look at the velocity formula. As previously stated, velocity is defined as a change in an objects displacement over time. Simply said, velocity is a measurement of how long it takes an object to go in a specific direction. Furthermore, it is proportional to the displacement and inversely proportional to travel time. Its unit is also the meter per second . The formula of velocity is given below:

We know that s = r ,v = r /t

Now we replace /t by .

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## What Is Constant Velocity

When you read mechanics, you will hear the words **uniform velocity** or **constant velocity**.

These two words mean the same thing. **That is, constant velocity is called uniform velocity**. There are many concepts of mechanics hidden in this Uniform Velocity word. So, in this tutorial, we will discuss in depth about constant-velocity through graphical representation.

Before discussing in detail you need to understand when a vector quantity is constant because velocity is a vector quantity.

## The Average Velocity Formula And Velocity Units

The average velocity formula describes the relationship between the length of your route and the time it takes to travel. For example, if you drive a car for a distance of 70 miles in one hour, your average velocity equals 70 mph. In the previous section, we have introduced the basic velocity equation, but as you probably have already realized, there are more equations in the velocity calculator. Let’s list and organize them below:

final velocity = initial velocity + acceleration * time

average velocity = velocityâ * timeâ + velocityâ * timeâ + …

You should use the average velocity formula if you can divide your route into few segments. For example, you drive a car with a speed of 25 mph for 1 h in the city and then reach 70 mph for 3 h on the highway. What is your average velocity? With the velocity calculator, you can find that it will be about 59 mph.

From the above equations, you can also imagine **what are velocity units**. British imperial units are feet per second ft/s and miles per hour mph. In the metric SI system the units are meters per second m/s and kilometers per hour km/h. Remember you can always easily switch between all of them in our tool!

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## Initial And Final Velocity

Initial velocity describes how fast an object travels when gravity first applies force on the object. On the other hand, the final velocity is a vector quantity that measures the speed and direction of a moving body after it has reached its maximum acceleration.

#### How to find the final velocity?

Finding the final velocity is simple with a few calculations and basic conceptual knowledge.

## How To Find The Final Velocity

The final velocity of an object is equal to its initial velocity plus acceleration multiplied by the time it travelled, and can be given as:

v = u + at

a = acceleration

t = time

As the equation shows for a given object, you can calculate its final velocity by adding its initial velocity to the acceleration due to force multiplied by the time for which the force applied to it. The delta in front of the time displays the change in time, which can be written as tv tu. Here, tv tu is the time elapsed from u to v.

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## How To Tell Speed And Velocity Apart

Speed and velocity both measure an objects rate of motion. However, speed is a scalar quantity, which means that it can be described with a numerical value. Velocity is a vector quantity, which depends on direction as well as magnitude. Read these definition for more information:

- speed – the rate of distance traveled by a moving object over time
- velocity – the rate of displacement of a moving object over time

Basically, an objects speed tells you how fast its going. Its velocity tells you how fast its going in a certain direction. You use speed measurements in your daily life, but physicists depend on velocity measurements more frequently in their work.

## What’s The Difference Between Speed And Velocity

When describing the motion of objects in terms of distance, time, and direction, physicists use the basic quantities of speed and velocity. Two terms, two distinct meanings. Yet, not uncommonly, we hear these terms used interchangeably. So, whats the difference? Why is it incorrect to use the terms *speed* and *velocity* interchangeably?

The reason is simple. **Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an objects movement**. Put another way, speed is a scalar value, while velocity is a vector. For example, 50 km/hr describes the speed at which a car is traveling along a road, while 50 km/hr *west* describes the velocity at which it is traveling.

The mathematical calculation for speed is relatively straightforward, wherein the average speed of an object is calculated by dividing the distance traveled by the time it took the object to travel the distance. Velocity, on the other hand, is more complicated mathematically and can be calculated in different ways, depending on what information is available about the objects motion. In its simplest form, average velocity is calculated by dividing change in position by change in time .

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## What Is Average Velocity

Average velocity is a vector quantity. Average velocity is defined as the change in position or displacement divided by the time intervals in which the displacement occurs.The average velocity can be positive or negative depending upon the sign of the displacement. The SI unit of average velocity is meters per second .

## Speed Velocity And Acceleration

Speed, velocity, and acceleration are all related to each other, though they represent different measurements. Be careful not to confuse these values with each other.

**Speed**, according to its technical definition, is a scalar quantity that indicates the rate of motion distance per time. Its units are length and time. Put another way, speed is a measure of distance traveled over a certain amount of time. Speed is often described simply as the distance traveled per unit of time. It is how fast an object is moving.**Velocity**is a vector quantity that indicates displacement, time, and direction. Unlike speed, velocity measures*displacement,*a vector quantity indicating the difference between an object’s final and initial positions. Speed measures distance, a scalar quantity that measures the total length of an object’s path.**Acceleration**is defined as a vector quantity that indicates the rate of change of velocity. It has dimensions of length and time over time. Acceleration is often referred to as “speeding up”, but it really measures changes in velocity. Acceleration can be experienced every day in a vehicle. You step on the accelerator and the car speeds up, increasing its velocity.

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## Velocity Is Speed With A Direction

In physics, we often associate a **direction** with physical quantities. For example, it’s nice to know the direction in which an object is moving or in what direction a **force** is applied to an object. To do this, we employ the concept of **vectors**. I strongly suggest that if you have not, you take a look at the vectors section before working through this one. It’s absolutely crucial in physics to have a good working understanding of vectors.

$$\text = \frac}}$$

#### $$v = \frac$$

Just like speed, this is an average velocity over time t. We cannot know anything about the velocity at any instant in time from this definition.

But: velocity has a *direction*.

**Velocity** is the vector version of **speed**. Velocity is speed with a specified direction.

A velocity vector is an **arrow** that points in the direction of motion and has a length proportional to the speed. We call the speed the **magnitude** of the velocity vector.

The only two things of importance about vectors is **length** and **direction**. Velocity vectors can be moved around in a plane or in 3-D space at will for the convenience of making calculation easier, so long as length and direction aren’t affected.

**Note:** Before you work through this section, you might want to work through the vectors section, and possibly the speed section.

#### A word about vector notation

## Solved Examples For Velocity Formula Physics

Q.1: A boat is in a 1000 m race, and it crosses the starting line at its full speed. Then it reaches the finish line within exactly 1 minute and 20 seconds. Determine the velocity of the boat in meter per second.

Solution: The initial position will be the starting line, which we can get the value,

The finish line will be 1000 m from the start,

Thus \

The time taken by the boat to travel that distance, t = 60 + 20 sec = 80.0 sec.

The velocity can be found using the formula as:

= 12.5 meter per sec.

Therefore, the velocity will be \. Its direction will be towards the finish line.

Q.2: A submarine descends 150 meters in 5 seconds. Find out the Velocity of the submarine.

Solution: Known parameters are,

Distance travelled, d = 150 meter,

Time taken, t = 5 seconds

V= 30 m per sec.

Therefore of the velocity of the submarine will be \

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## Examples: Airplane Velocity Vectors

Consider an airplane that can travel at a speed of 150 Km/h in still air. That would give it a velocity vector of 150 Km/h in length pointed in its direction of travel. Now add in a 30 Km/h headwind. The situation is shown below. The net forward velocity of the plane is the sum of 150 Km/h and -30 Km/h, or 120 Km/h in the direction of travel.

Now let’s turn that headwind into a tailwind, or pushing wind. The vector diagram is shown below. This time the 30 Km/h wind vector adds to the velocity of the plane, for a total velocity of 180 Km/h.

That’s why a flight across the United States from west to east is usually faster than a flight from east to west. The prevailing wind moves from west to east.

Now let’s get a little fancier. How about a **cross-wind**, or a wind that comes from 90Ë from the direction of travel from the right or left.

To add these two vectors, just use the **Pythagorean theorem**. You can see that the direction of travel will be slightly to the right of where the plane is steering, and it’s velocity will be 6 Km/h faster than without the crosswind.

Finally, let’s let the wind hit the plane at an odd angle, so that if we want the new velocity vector, we have to solve a law of cosines problem. If you don’t know the LOC, don’t worry about it right now.

This is basically how we navigate planes without more sophisticated equipment like radio and radar.