Name: how velocity changes create acceleration
Uploaded: 2023-04-30T10:51:43.000Z
Duration: 1 min 30 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

Acceleration Vectors

Скорость является векторной величиной и представляет собой скорость с направлением. Ускорение существует, когда происходит изменение скорости — либо за счет увеличения или замедления, либо при изменении направления, либо при одновременном изменении того и другого.
Математический способ выражения ускорения — это изменение скорости с течением времени.
Предположим, что объект движется с постоянной скоростью. Во время выполнения поворота он замедляется. Его мгновенная скорость изменяется как по величине, так и по направлению. Пусть мгновенные векторы скоростей, расположенные в точках P1 и P2, являются векторами v1 и v2.
Путем вычитания векторов получается изменение скорости, дельта-вектор v.
Теперь направление среднего вектора ускорения будет в направлении изменения скорости. Средний вектор ускорения задается отношением между вектором Δ v и Δt.
Когда мы рассматриваем меньшие интервалы времени, позиция P2 приближается к P1. В этот момент, когда Δt стремится к нулю, среднее ускорение приближается к мгновенному ускорению.

Векторы ускорения

В повседневной беседе ускорение означает увеличение скорости. Ускорение является вектором, направленным так же, как изменение скорости, Δ v, поэтому чем больше ускорение, тем больше изменение скорости за определённое время. Поскольку скорость является вектором, она может меняться по величине, направлению или по обоим параметрам. Таким образом, ускорение представляет собой изменение скорости или направления или и того, и другого. Например, если бегун, двигаясь со скоростью 10 км/ч на восток, замедляется до остановки, меняет направление и продолжает бежать со скоростью 10 км/ч на запад, его скорость изменяется вследствие изменения направления, хотя величина скорости одинакова в обоих направлениях. Таким образом, ускорение происходит, когда скорость изменяется по величине (увеличение или уменьшение скорости), по направлению или по обоим параметрам.

Вектор ускорения — это мгновенное ускорение, и он может быть получен из производной функции скорости по времени. Ускорение сильно варьирует в зависимости от разных объектов и не имеет ничего общего с размером объекта или его массой. Ускорение также может существенно изменяться со временем во время движения объекта. Например, у гоночного автомобиля большое ускорение сразу после старта, но затем оно постепенно уменьшается, когда автомобиль достигает постоянной скорости. Его среднее ускорение может существенно отличаться от мгновенного ускорения в определённый момент времени во время движения.

Этот текст адаптирован из <a href="https://openstax.org/books/university-physics-volume-1/pages/4-2-acceleration-vector">Openstax, University Physics Volume 1, Section 4.2: Acceleration Vector.</a>

В повседневном разговоре ускорение означает ускорение. Ускорение является вектором в том же направлении, что и изменение скорости, Δv, следовательно, ...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Motion in Two or Three Dimensions

Движение в двух или трех измерениях

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

how velocity changes create acceleration

Acceleration describes how velocity changes over time. In physics, acceleration is a vector, which means it has both size and direction. It points in the same direction as the change in velocity, written as Δv. The larger the acceleration, the larger the change in velocity over a given time.

Because velocity is a vector, it can change in more than one way. An object can speed up, slow down, change direction, or do both at once. A runner traveling 10 km/h due east who stops, turns around, and then runs 10 km/h due west has changed velocity because the direction changed, even though the speed is the same. That change in direction still counts as acceleration.

The acceleration vector is the instantaneous acceleration at a specific moment. It can be found from the derivative of the velocity function with respect to time. Acceleration can also change during motion. A drag racer may have a large acceleration right after the start and then a smaller acceleration as the car reaches constant velocity.

Acceleration is not tied to the size of an object or its mass. Different objects can have very different accelerations. Average acceleration can also be different from instantaneous acceleration at one moment in time. This makes acceleration an important way to describe how motion changes from instant to instant.

How Velocity Changes Create Acceleration

position and displacement vectors

Describing Motion with Position Changes

Describing motion starts with position. Position tells where an object is at a particular time. It must be measured relative to a frame of reference, which is an arbitrary set of axes used to describe position and motion. Earth is often used as a frame of reference. It helps describe an object’s location in relation to stationary objects on Earth. Many important motions also take place in two dimensions, or in a plane. In those cases, position, velocity, and acceleration can each be described...

average and instantaneous velocity vectors

average-and-instantaneous-velocity-vectors

Position Change and Instant Velocity

Position change and instant velocity are key ideas in kinematics. To describe motion, time must be included. Time tells us where an object is and how fast it is moving. The speed of an object comes from how its position changes with time. Each position is tied to a specific time. When the details of motion at each instant are not important, the rate is given as average velocity. Average velocity is a vector. It equals the total displacement between two points divided by the elapsed time. Real...

acceleration vectors

Acceleration describes how velocity changes over time. In physics, acceleration is a vector, which means it has both size and direction. It points in the same direction as the change in velocity, written as Δv. The larger the acceleration, the larger the change in velocity over a given time. Because velocity is a vector, it can change in more than one way. An object can speed up, slow down, change direction, or do both at once. A runner traveling 10 km/h due east who stops, turns around, and...

direction of acceleration vectors

Negative Acceleration and Motion Reversal

Acceleration describes a change in velocity. That change can be a change in speed, a change in direction, or both. The acceleration vector points in the direction of the velocity change, not always in the direction the object is moving. When an object slows down, its acceleration points opposite to its motion. This is often called deceleration. The term can be confusing in physics because deceleration is not a vector. It does not give a direction relative to a coordinate system, so the correct...

projectile motion

Projectile Paths Under Gravity

Projectile motion describes the path of an object thrown into the air under Earth’s gravity. The object is called a projectile, and its curved path is called the trajectory. This motion appears in many real situations, such as fireworks, a golf ball in flight, meteors entering Earth’s atmosphere, and bullets being fired. When a falling object has no horizontal movement, it is described as one-dimensional projectile motion. When motion includes both horizontal and vertical parts, it is...

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projectile motion: equations

Solving Projectile Motion with Components

Projectile motion can be solved by breaking the motion into horizontal and vertical components. This approach is used for common examples like a basketball throw, an arrow shot from a bow, and kids jumping into a pool. The motion is then analyzed along the x-axis and y-axis. Start by separating displacement into x and y parts. The horizontal and vertical parts of velocity are also separated. If the projectile has speed v and direction θ relative to the horizontal, the vertical component is...

projectile motion: example

Projectile Motion in Sports and Orbit

Projectile motion helps explain both sports throws and motion near Earth. A javelin thrower uses this idea to send the javelin as far as possible. The thrower also takes a short run-up to increase the initial speed of the javelin. For a projectile on level ground, the range is the horizontal distance it travels. The range is largest at a 45° angle, so javelin throwers try to release the javelin as close to that angle as possible. In this case, the range equation assumes the distance is very...

uniform circular motion

Centripetal Acceleration in Circular Motion

Uniform circular motion describes motion in a circle at constant speed. An object follows a curved path, but its speed does not change. The motion of a point on a propeller spinning at a steady rate and the second, minute, and hour hands of a watch are common examples. Even with constant speed, these objects are still accelerating. That idea can seem surprising because in one-dimensional motion, constant speed means zero acceleration. In two- and three-dimensional motion, a particle can...

non-uniform circular motion

Circular Motion with Changing Speed

Circular motion can happen with changing speed. In this case, the object still follows a circular path, but it may speed up or slow down as it moves. When speed changes during circular motion, the motion is called non-uniform circular motion. This adds tangential acceleration, which points along the path of motion and shows a change in speed. Centripetal acceleration is still present in circular motion. It describes the time rate of change of the direction of the velocity vector and points...

relative velocity in one dimension

Relative Motion in a Train and Earth

Relative motion depends on the reference frame used to measure velocity. A reference frame is the point of view from which motion is described. In many examples, Earth is the reference frame. If someone is said to be sitting in a train moving east at 10 m/s, that speed is measured relative to Earth.

relative velocity in two dimensions

Adding Velocities Across Reference Frames

Relative velocity describes motion as measured from a chosen reference frame. It can also describe the motion of one reference frame compared with another. In two dimensions, this idea helps track how position and velocity change from frame to frame. Consider a particle P and two reference frames, S and S′. The position of the origin of S′, measured in S, and the position of P, measured in S′, can be combined with vector addition to find the position of P in S. This relation shows how motion...

key terms and concepts

Learn how acceleration depends on changes in velocity, including speeding up, slowing down, and changing direction, with a runner and drag racer example.

How Velocity Changes Create Acceleration | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

PS.Phy.1.2

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Ohio’s Learning Standards and Model Curriculum

Forces And Motion

Motion

Motion Graphs

Tennessee Academic Standards

High School

Motion and Stability: Forces and Interactions

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Virginia  Standards of Learning

HIgh School

PS.8

PS.8.a

PH.2

PH.2.a

PH.2.c

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PHYS.5

PHYS.5.D

Arizona Science Standards

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HS+Phy.P3U1.3

Alabama Course of Study Science

9-12.P.1.1

9-12.P.1.1.c

Florida Department of Education

SC.912.P.12

SC.912.P.12.2

Georgia Standards of Excellence

SPS8.

Describing Motion

SP1.

Two-Dimensional Motion

Position and Displacement

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Average Velocity

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Instantaneous Velocity - I

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Instantaneous Velocity - II

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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

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Direction of Acceleration Vectors

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Construct an explanation to compare simple series and parallel circuits in terms of Ohm's Law.

PS.PSc.6.2

Continuity Equation

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Boundary Conditions for Current Density

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Electrical Conductivity

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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

Magnets are commonly found in everyday objects, such as toys, hangers, elevators, doorbells, and computer devices. Experimentation on these magnets shows ...

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Magnetic Field Lines

The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the ...

Magnetic Flux

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Motion Of A Charged Particle In A Magnetic Field

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Magnetic Force

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Magnetic Force On A Current-Carrying Conductor

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magnetic-force-on-current-carrying-wires-example

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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The Hall Effect

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Biot-Savart Law

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Solenoids

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Magnetic Field of a Solenoid

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Toroids

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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.

How Velocity Changes Create Acceleration

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