Name: average velocity and average speed
Uploaded: 2023-04-30T10:49:50.000Z
Duration: 1 min 12 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.4.1

Average Velocity

A velocidade média informa a rapidez com que um objeto está se movendo ao longo do tempo e é definida como o deslocamento total entre dois pontos dividido pelo tempo necessário para viajar entre eles.
Por exemplo, se p1 e p2 são as posições de um objeto no tempo t1 e t2, então a velocidade x média é dada como <span style="font-size: 11pt; font-family: Arial; color: rgb(0, 0, 0); background-color: transparent; font-variant-numeric: normal; font-variant-east-asian: normal; vertical-align: baseline; white-space: pre-wrap;">Δx dividido por <span style="font-size: 11pt; font-family: Arial; color: rgb(0, 0, 0); background-color: transparent; font-variant-numeric: normal; font-variant-east-asian: normal; vertical-align: baseline; white-space: pre-wrap;">Δt. Observe que a velocidade média é uma quantidade vetorial e pode ser positiva ou negativa, dependendo se o deslocamento é positivo ou negativo.
O gráfico de posição versus tempo é uma forma pictórica de representar como um objeto muda de posição com o tempo. Ele plota o tempo no eixo x e a posição no eixo y. Portanto, a velocidade média x do objeto é igual à inclinação da linha p1, p2.
A velocidade média é definida como a distância total percorrida por um corpo dividida pelo tempo necessário para completar a distância. Ao contrário da velocidade média, é uma quantidade escalar.

velocidade média

Para calcular as outras grandezas físicas na cinemática, precisamos introduzir a variável tempo. A variável tempo nos permite não apenas afirmar a posição do objeto durante seu movimento, mas também quão rápido ele está se movendo. A velocidade com que um objeto está se movendo é dada pela taxa em que a posição muda com o tempo. Para cada posição xi, atribuímos um tempo específico ti. Se os detalhes do movimento em cada instante não forem importantes, a taxa é normalmente expressa como a velocidade média. Essa grandeza vetorial é simplesmente o deslocamento total entre dois pontos, ∆x, dividido pelo tempo despendido para viajar entre eles, ∆t. A velocidade média é um vetor e pode ser positiva ou negativa, dependendo das posições inicial e final. A expressão para a velocidade média é dada por:

<img alt="Equation1" src="/files/ftp_upload/12617/12617_Equation_1.png" style="height: 35px;" />

A velocidade escalar média não é, necessariamente, igual à magnitude da velocidade média. Por exemplo, se uma viagem começa e termina no mesmo local, o deslocamento total é zero e, portanto, a velocidade média é zero. A velocidade escalar média, no entanto, não é zero, porque a distância total percorrida é maior que zero. Se fizermos uma viagem de carro de 300 km e precisarmos estar em nosso destino em um determinado horário, estaríamos interessados em nossa velocidade média. O odômetro de um carro mede a distância total percorrida. Portanto, a distância total percorrida pelo carro dividida pelo tempo total fornece a velocidade escalar média do carro.

Por exemplo, o trem Maglev de Shanghai conecta Longyang Road ao Aeroporto Internacional de Pudong, que é uma distância de 30 km. A viagem leva em média 8 minutos. Qual é a velocidade média do trem Maglev?

As quantidades conhecidas são a distância e o tempo. A quantidade desconhecida, a velocidade média, é a distância total dividida pelo tempo. Assim, a velocidade média do trem Maglev é de 225 km/h.



Este texto foi adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/3-1-position-displacement-and-average-velocity">Openstax, University Physics Volume 1, Section 3.1: Position, Displacement, and Average Velocity</a>.

Velocidade média

Para calcular as outras grandezas físicas na cinemática, devemos introduzir a variável tempo. A variável tempo nos permite não apenas indicar a posição ...

Education

JoVE Core

Physics

Física

Unit 1

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Motion Along a Straight Line

Movimento Retilíneo

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

average velocity and average speed

Average velocity and average speed help describe motion in kinematics. To compare motion over time, we use the time variable. Time lets us track an object’s position and how fast that position changes.

For motion between two points, each position x_i is paired with a time t_i. When the details of motion at each instant are not important, we use average velocity. Average velocity is a vector quantity, so it includes direction. It is found by dividing total displacement, Δx, by the time interval, Δt.

Because it is a vector, average velocity can be positive or negative. The sign depends on the object’s initial and final positions. Average speed is different. It is the total distance traveled divided by the elapsed time, so it is not necessarily the same as the magnitude of average velocity.

A round trip shows the difference clearly. If an object starts and ends at the same place, its total displacement is zero, so its average velocity is zero. Its average speed is not zero, because the total distance traveled is still greater than zero. On a road trip of 300 km, average speed is the quantity that matters if you need to reach a destination by a certain time. A car’s odometer measures total distance traveled, so dividing that distance by total time gives the car’s average speed.

The Shanghai Maglev train gives another example. It travels from Longyang Road to Pudong International Airport over a distance of 30 km. The trip takes about 8 minutes on average. Using the distance and time, the train’s average velocity is 225 km/hr.

Average Velocity and Average Speed

position and displacement

Reference Frames and Motion in a Line

Position in straight-line motion depends on a frame of reference. A frame of reference is an arbitrary set of axes used to describe an object’s position and motion. It gives meaning to where something is located at a particular time. Earth is often used as the reference frame. In that case, we describe an object’s position relative to stationary objects on Earth. A rocket launch can be described this way. A cyclist’s position can also be described relative to the buildings they pass. <br...

average velocity

Average velocity and average speed help describe motion in kinematics. To compare motion over time, we use the time variable. Time lets us track an object’s position and how fast that position changes. For motion between two points, each position x_i is paired with a time t_i. When the details of motion at each instant are not important, we use average velocity. Average velocity is a vector quantity, so it includes direction. It is found by dividing total displacement, Δx, by the time...

instantaneous velocity - i

Instantaneous Speed and Direction

Instantaneous velocity describes how fast an object is moving at a specific instant. It gives the motion of a particle at one point in time or at one point along its path. Average velocity over a time interval cannot show this level of detail. Instantaneous velocity, often written as v x , is the limit of average velocity as the elapsed time approaches zero. It can also be found as the derivative of x with respect to t . Like average velocity, it is a vector with dimensions of length per unit...

instantaneous velocity - ii

Instantaneous Velocity from Position Graphs

Instantaneous velocity describes how fast an object is moving at a specific moment along its path. It is the limit of average velocity as the elapsed time approaches zero. It can also be written as the derivative of displacement with respect to time. Like average velocity, instantaneous velocity is a vector, so it has both size and direction. Its units are length per unit time. Instantaneous velocity can be positive or negative. A position-time graph can show it at any point on the motion...

average acceleration

Average Acceleration and Velocity Change

Average acceleration describes how velocity changes over time. In physics, acceleration is not just about speeding up. It also includes slowing down and changing direction. Since velocity is a vector, it has both magnitude and direction. A change in velocity can come from a change in speed, a change in direction, or both. For example, a runner may travel at 10 km/h due east, stop, reverse direction, and then continue at 10 km/h due west. Even though the speed is the same, the velocity has...

instantaneous acceleration

Negative Acceleration and Instant Speed Change

Acceleration shows how velocity changes, and it does not always point in the same direction as motion. When an object slows down, its acceleration points opposite to its motion. This is often called deceleration, but that term can cause confusion because deceleration is not a vector and does not point in a specific direction in a coordinate system. A subway train is a simple example. When the train slows down, it is still accelerating, but the acceleration points opposite to the direction it...

kinematic equations - i

Velocity from Constant Acceleration

Velocity from constant acceleration shows how an object’s speed and direction change when the acceleration stays the same. The first kinematic equation connects initial velocity, acceleration, and time for motion with constant acceleration. It helps describe how velocity changes at a steady rate throughout the motion. The equation matches common sense in several cases. If acceleration is zero, the final velocity is the same as the initial velocity, so the object keeps a constant velocity. If...

kinematic equations - ii

Using the Second Kinematic Equation

The second kinematic equation relates an object’s final position to its initial position, its starting velocity, and the extra distance gained as velocity changes. It is used only when acceleration stays constant during the motion. That makes it useful for straight-line motion problems with a steady rate of acceleration. A car merging onto a 200 m freeway ramp is a good example. In the example, the car starts at 10 m/s and accelerates at 2 m/s². The known values are the distance, the initial...

kinematic equations - iii

Constant-Acceleration Kinematics Formulas

Constant-acceleration kinematics formulas connect an object’s motion when acceleration stays the same. They help describe how velocity and position change over time. These equations are useful for solving motion problems and for understanding the relationships among distance, time, velocity, and acceleration. The third kinematic equation does not use time as a variable. Instead, it gives final velocity in terms of acceleration and the distance over which that acceleration acts. The fourth...

kinematic equations: problem solving

Solving Constant Acceleration Motion Problems

Solving one-dimensional motion problems with constant acceleration starts with identifying the known quantities and choosing the right kinematic equation. A kinematic equation is a motion formula that relates displacement, velocity, acceleration, and time. Depending on what is known and unknown, you may need one equation or two equations to find the answer. In many problems, the number of equations needed matches the number of unknowns. Two-body pursuit problems are different. They always...

free-falling bodies: introduction

Gravity and Free-Fall Motion

Gravity and free-fall motion explain how objects move when only Earth’s gravity acts on them. In free-fall, the motion is caused by gravitational force, and air resistance is neglected. This means the object accelerates toward Earth’s center. This result is surprising because everyday experience includes friction and air resistance. We often expect lighter objects to fall more slowly than heavier ones. People held that idea until Galileo Galilei proved that mass does not change the...

free-falling bodies: example

Gravity-Driven Free Fall Motion

Gravity-driven free fall motion is the motion of an object when gravity is the only force acting on it and air resistance is absent. In this case, the object is in free-fall. The acceleration due to gravity stays constant, no matter how much the object weighs. Free-fall is not limited to objects moving straight down. It also includes motion that is affected only by gravity. Because the acceleration is constant, the motion can be described with kinematic equations. Objects dropped from the...

velocity and position by graphical method

velocity-and-position-by-graphical-method

Acceleration Graphs for Motion Prediction

Acceleration graphs can be used to find velocity and position over time. The area under an acceleration-time graph gives the change in velocity. The area under a velocity-time graph gives the change in position, or displacement. A real example is an airplane using an inertial navigation system. Before takeoff, the pilot enters the airplane’s initial position and velocity. The system then uses acceleration data to calculate the airplane’s velocity and position during flight. When acceleration...

velocity and position by integral method

Finding Motion from Acceleration Data

Velocity and position can be found from acceleration using integral calculus. When acceleration is known as a function of time, the velocity function comes from integrating acceleration. The position function then comes from integrating velocity. For constant acceleration, these integral steps match the first and second kinematic equations for velocity and position. The example in this lesson uses a motorboat that is moving at 5.0 m/s and then begins to slow down as it approaches the dock. Its...

key terms and concepts

Learn how average velocity and average speed are calculated from displacement, distance, and time, with simple motion examples for high school physics.

Average Velocity and Average Speed | JoVE K12

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JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

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Ohio’s Learning Standards and Model Curriculum

Forces And Motion

Motion

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PS.8

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Arizona Science Standards

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HS.P3

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Alabama Course of Study Science

Motion and Stability: Forces and Interactions

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Florida Department of Education

SC.912.P.12

SC.912.P.12.2

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PHYS.5

PHYS.5.A

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Chemistry and Physics

IPC.5

IPC.5.A

Georgia Standards of Excellence

SPS8.

Describing Motion

SP1.

One-Dimensional Motion

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position ...

Instantaneous Velocity - I

The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To ...

Instantaneous Velocity - II

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object ...

Average Acceleration

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Instantaneous Acceleration

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Position and Displacement Vectors

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average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

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Direction of Acceleration Vectors

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Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

Force and Momentum

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Analyze and interpret data to explain the motion of an object moving with a constant velocity or that is accelerating.

Electrical Current

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Drift Velocity

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Current Density

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Resistivity

When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The ...

Resistance

When a current moves through any conductor, the conductor causes some level of difficulty for the current to flow. The measure of that difficulty is known ...

Ohm's Law

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PS.PSc.6.2

Continuity Equation

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Theory of Metallic Conduction

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Obtain, evaluate, and communicate information to explain how current is affected by changes in composition, length, temperature, and diameter of wire.

PS.PSc.6.3

Magnetism

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Magnetic Fields

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Magnetic Field Lines

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motion-of-a-charged-particle-in-a-magnetic-field

Motion Of A Charged Particle In A Magnetic Field

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Magnetic Force On A Current-Carrying Conductor

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Magnetic Force On Current-Carrying Wires: Example

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Force On A Current Loop In A Magnetic Field

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Torque On A Current Loop In A Magnetic Field

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Divergence and Curl of Magnetic Field

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To evaluate the divergence of the ...

Use models to explain magnetism in terms of domains, interactions of poles, and magnetic fields.

PS.PSc.6.4

Analyze motion in terms of speed, velocity, acceleration, and momentum.

Average Velocity and Average Speed

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