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- What Is Velocity in Physics?
- Speed, Velocity, and Acceleration
- Acceleration
- Displacement, Velocity and Acceleration

## What Is Velocity in Physics?

The learning objectives in this section will help your students master the following standards:. In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Position and Speed of an Object, as well as the following standards:. In this section, students will apply what they have learned about distance and displacement to the concepts of speed and velocity.

Then ask them if they have heard the word velocity used. Explain that these words are often used interchangeably in everyday life, but their scientific definitions are different.

Tell students that they will learn about these differences as they read the section. Ask them to speculate about ways that speed is different from velocity.

After they share their ideas, follow up with questions that deepen their thought process, such as: Why do you think that? What is an example? How might apply these terms to motion that you see every day? There is more to motion than distance and displacement. In this section we will look at time , speed, and velocity to expand our understanding of motion.

A description of how fast or slow an object moves is its speed. Speed is the rate at which an object changes its location. Like distance, speed is a scalar because it has a magnitude but not a direction.

Because speed is a rate, it depends on the time interval of motion. When you describe an object's speed, you often describe the average over a time period.

Average speed , v avg , is the distance traveled divided by the time during which the motion occurs. You can, of course, rearrange the equation to solve for either distance or time.

Suppose, for example, a car travels kilometers in 3. Its average speed for the trip is. A car's speed would likely increase and decrease many times over a 3. Its speed at a specific instant in time, however, is its instantaneous speed. A car's speedometer describes its instantaneous speed. For example, suppose a car travels a distance of km.

Emphasize the importance in science to use correct terminology to avoid confusion and to properly communicate ideas. We know the distance the marble travels, 5.

We can use these values in the average speed equation. Average speed is a scalar, so we do not include direction in the answer. We can check the reasonableness of the answer by estimating: 5 meters divided by 2 seconds is 2.

Since 2. This is about the speed of a brisk walk, so it also makes sense. The distance is What was the average speed of the baseball? The vector version of speed is velocity. Velocity describes the speed and direction of an object.

As with speed, it is useful to describe either the average velocity over a time period or the velocity at a specific moment. Average velocity is displacement divided by the time over which the displacement occurs.

Furthermore, the variable v for velocity is bold because it is a vector, which is in contrast to the variable v for speed which is italicized because it is a scalar quantity. It is important to keep in mind that the average speed is not the same thing as the average velocity without its direction. Like we saw with displacement and distance in the last section, changes in direction over a time interval have a bigger effect on speed and velocity.

We cannot tell from the average velocity whether the passenger stopped momentarily or backed up before he got to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals such as those shown in Figure 2. If you consider infinitesimally small intervals, you can define instantaneous velocity , which is the velocity at a specific instant in time. Instantaneous velocity and average velocity are the same if the velocity is constant.

Earlier, you have read that distance traveled can be different than the magnitude of displacement. In the same way, speed can be different than the magnitude of velocity. For example, you drive to a store and return home in half an hour. Your average velocity, however, was zero because your displacement for the round trip is zero. This video reviews vectors and scalars and describes how to calculate average velocity and average speed when you know displacement and change in time.

This video does a good job of reinforcing the difference between vectors and scalars. Explain the use of small arrows over variables is a common way to denote vectors in higher-level physics courses. Caution students that the customary abbreviations for hour and seconds are not used in this video. Remind students that in their own work they should use the abbreviations h for hour and s for seconds. A student has a displacement of m north in s. What was the student's average velocity? We know that the displacement is m north and the time is s.

We can use the formula for average velocity to solve the problem. Since average velocity is a vector quantity, you must include direction as well as magnitude in the answer. Notice, however, that the direction can be omitted until the end to avoid cluttering the problem. Pay attention to the significant figures in the problem. The distance m has three significant figures, but the time interval s has only two, so the quotient should have only two significant figures.

Note the way scalars and vectors are represented. In this book d represents distance and displacement. Similarly, v represents speed, and v represents velocity.

A variable that is not bold indicates a scalar quantity, and a bold variable indicates a vector quantity. Vectors are sometimes represented by small arrows above the variable. Use this problem to emphasize the importance of using the correct number of significant figures in calculations. Some students have a tendency to include many digits in their final calculations. They incorrectly believe they are improving the accuracy of their answer by writing many of the digits shown on the calculator.

Point out that doing this introduces errors into the calculations. In more complicated calculations, these errors can propagate and cause the final answer to be wrong. Instead, remind students to always carry one or two extra digits in intermediate calculations and to round the final answer to the correct number of significant figures.

Layla jogs with an average velocity of 2. What is her displacement after 46 seconds? We know that Layla's average velocity is 2. We can rearrange the average velocity formula to solve for the displacement. The answer is about m east, which is a reasonable displacement for slightly less than a minute of jogging. A calculator shows the answer as We chose to write the answer using scientific notation because we wanted to make it clear that we only used two significant figures.

Dimensional analysis is a good way to determine whether you solved a problem correctly. Write the calculation using only units to be sure they match on opposite sides of the equal mark. Phillip walks along a straight path from his house to his school. How long will it take him to get to school if he walks m west with an average velocity of 1. We know that Phillip's displacement is m west, and his average velocity is 1.

We can calculate the time required for the trip by rearranging the average velocity equation. Here again we had to use scientific notation because the answer could only have two significant figures. Since time is a scalar, the answer includes only a magnitude and not a direction.

A bird flies with an average velocity of 7. It then pauses before flying with an average velocity of 6. In this simulation you will put your cursor on the man and move him first in one direction and then in the opposite direction. Keep the Introduction tab active. You can use the Charts tab after you learn about graphing motion later in this chapter.

Carefully watch the sign of the numbers in the position and velocity boxes. Ignore the acceleration box for now. Then see if you can do the opposite. This is a powerful interactive animation, and it can be used for many lessons. At this point it can be used to show that displacement can be either positive or negative. It can also show that when displacement is negative, velocity can be either positive or negative.

## Speed, Velocity, and Acceleration

It is expressed as distance moved d per unit of time t. Speed is thus the magnitude component of velocity. Velocity contains both the magnitude and direction components. Top athletic sprinters can run at Acceleration, symbol: a is defined as the rate of change of velocity. To accelerate an object is to change its velocity, which is accomplished by altering either its speed or direction like in case of uniform circular motion in relation to time. Acceleration can have positive and negative values.

Foundation Science for Engineers pp Cite as. So far our discussion has been about systems that are either at rest or in a state of uniform motion. This topic introduces the idea of accelerated motion but, for the moment, without any reference to the forces that cause it. Unable to display preview. Download preview PDF. Skip to main content.

What is instantaneous speed? Page Velocity. Velocity is a description of an object's speed and direction.

## Acceleration

In mechanics , acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities in that they have magnitude and direction. The magnitude of an object's acceleration, as described by Newton's Second Law , [3] is the combined effect of two causes:. For example, when a vehicle starts from a standstill zero velocity, in an inertial frame of reference and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an acceleration occurs toward the new direction and changes its motion vector.

Just as distance and displacement have distinctly different meanings despite their similarities , so do speed and velocity. Speed is a scalar quantity that refers to "how fast an object is moving. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time. Contrast this to a slow-moving object that has a low speed; it covers a relatively small amount of distance in the same amount of time. An object with no movement at all has a zero speed.

### Displacement, Velocity and Acceleration

When an object moves in a straight line at a steady speed, you can calculate its average speed if you know how far it travels and how long it takes. The following equation shows the relationship between average speed, distance moved and time taken:. For example, a car travels m in 20 s. Its average speed is:. A man runs after a bus. The man runs 25 m in 6 s.

In physics, however, they are distinct quantities. Speed is a scalar quantity and has only magnitude. Velocity, on the other hand, is a vector quantity and so has both magnitude and direction.

#### Accessibility links

Velocity is defined as a vector measurement of the rate and direction of motion. Put simply, velocity is the speed at which something moves in one direction. The speed of a car traveling north on a major freeway and the speed a rocket launching into space can both be measured using velocity. As you might have guessed, the scalar absolute value magnitude of the velocity vector is the speed of motion. In calculus terms, velocity is the first derivative of position with respect to time.

The learning objectives in this section will help your students master the following standards:.

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Подними, говорю. Беккер терял терпение. А ведь он мог быть сейчас в Смоки-Маунтинс, со Сьюзан. Что он делает здесь, в Испании, зачем спорит с этим психованным подростком. Беккер резким движением взял парня под мышки, приподнял и с силой посадил на столик.

*Тишина. Он тихонько толкнул дверь, и та отворилась.*

Должно быть, где-то замыкание. Желтый сигнал тревоги вспыхнул над шифровалкой, и свет, пульсируя, прерывистыми пятнами упал налицо коммандера. - Может, отключить его самим? - предложила Сьюзан. Стратмор кивнул. Ему не нужно было напоминать, что произойдет, если три миллиона процессоров перегреются и воспламенятся.

- Позволь мне кое-что проверить, - сказала она, перелистывая отчет. Найдя то, что искала, Мидж пробежала глазами цифры и минуту спустя кивнула: - Ты прав, Чед. ТРАНСТЕКСТ работал на полную мощность. Расход энергии даже чуть выше обычного: более полумиллиона киловатт-часов с полуночи вчерашнего дня. - И что все это .

* Просто неформальная дипломатическая любезность, - солгал .*

Стратмор ответил ей тоном учителя, терпеливого и умеющего держать себя в руках: - Да, Сьюзан, ТРАНСТЕКСТ всегда найдет шифр, каким бы длинным он ни. - Он выдержал длинную паузу. - Если только… Сьюзан хотела что-то сказать, но поняла, что сейчас-то Стратмор и взорвет бомбу. Если только -. - Если только компьютер понимает, взломал он шифр или .

Боюсь, вы опоздали, - внушительно заявил Беккер и прошелся по номеру. - У меня к вам предложение. - Ein Vorschlag? - У немца перехватило дыхание. - Предложение. - Да.

Коламбия пикчерз было гораздо дешевле снять эту картину в Испании, нежели в Египте, а мавританское влияние на севильскую архитектуру с легкостью убедило кинозрителей в том, что перед их глазами Каир. Беккер перевел свои Сейко на местное время - 9. 10 вечера, по местным понятиям еще день: порядочный испанец никогда не обедает до заката, а ленивое андалузское солнце редко покидает небо раньше десяти. Несмотря на то что вечер только начинался, было очень жарко, однако Беккер поймал себя на том, что идет через парк стремительным шагом.

А то ты не знаешь. Беккер пожал плечами. Парень зашелся в истерическом хохоте.

* Speed is the distance traveled divided by the time traveled. V = d. / t * Acceleration is the rate at which velocity changes.

Distance and displacement might seem similar at first but in fact are two very different things.