Name: position change and instant velocity
Uploaded: 2023-04-30T10:51:36.000Z
Duration: 1 min 12 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

motion-and-stability-forces-and-interactions

Motion and Stability- Forces and Interactions

PS.PSc.4.1

average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

Die durchschnittliche Geschwindigkeit wird als Verhältnis der Verschiebung zum Zeitintervall während dieser Verschiebung angegeben. In einem zweidimensionalen Raum stellt der Verschiebungsvektor Δr die Positionsänderung dar.
Wenn die Geschwindigkeit zu einem bestimmten Zeitpunkt berücksichtigt wird, nähert sich die verstrichene Zeit Null. Nun nähert sich die Grenze der Durchschnittsgeschwindigkeit der Momentangeschwindigkeit und ist gleich der Ableitung des Ortsvektors in Bezug auf die Zeit.
Die Richtung des momentanen Geschwindigkeitsvektors an einem beliebigen Punkt verläuft immer entlang einer Linie, die an diesem Punkt tangential zum Pfad verläuft.
Die Komponenten der Geschwindigkeit in einem zweidimensionalen Raum sind die Zeitableitungen der Koordinaten x und y. Somit ist der momentane Geschwindigkeitsvektor die Summe, an der zwei Einheitsvektoren beteiligt sind.
Bei der Beschreibung einer 3-dimensionalen Bewegung ist auch die z-Achse beteiligt, und der Geschwindigkeitsvektor wird mit Hilfe von drei Einheitsvektoren dargestellt.
Im momentanen Geschwindigkeitsvektor stellt die Größe die Geschwindigkeit des Objekts dar.

durchschnittliche und momentane geschwindigkeitsvektoren

Um andere physikalische Größen in der Kinematik zu berechnen, muss die Zeitvariable eingeführt werden. Die Zeitvariable ermöglicht es uns nicht nur, den Ort eines Objekts (seine Position) während seiner Bewegung anzugeben, sondern auch, wie schnell es sich bewegt. Die Geschwindigkeit, mit der sich ein Objekt bewegt, wird durch die Rate angegeben, mit der sich die Position mit der Zeit ändert. Für jede Position wird eine bestimmte Zeit zugewiesen. Wenn die Details der Bewegung in jedem Augenblick nicht wichtig sind, wird die Rate in der Regel als durchschnittliche Geschwindigkeit v ausgedrückt. Dieser Geschwindigkeitsvektor ist einfach die Gesamtveränderung zwischen zwei Punkten geteilt durch die Zeit, die benötigt wird, um zwischen ihnen zu reisen und ist auch als verstrichene Zeit bekannt.

Da sich Objekte in der realen Welt kontinuierlich im Raum und in der Zeit bewegen, ist die Durchschnittsgeschwindigkeit eines Objekts an einem einzigen Punkt ein wichtiger Parameter. Die Größe, die uns sagt, wie schnell sich ein Objekt entlang seines Pfades bewegt, wird als Momentangeschwindigkeit bezeichnet, oft einfach als Durchschnittsgeschwindigkeit bezeichnet. Es handelt sich um die Durchschnittsgeschwindigkeit zwischen zwei Punkten auf einem Pfad, bei dem die Zeit (und daher die Veränderung des Orts) zwischen den beiden Punkten gegen null strebt. Wie die durchschnittliche Geschwindigkeit ist die Momentangeschwindigkeit ein Vektor mit den Dimensionen Länge pro Zeit.

Dieser Text ist angepasst von <a href="https://openstax.org/books/university-physics-volume-1/pages/4-1-displacement-and-velocity-vectors">Openstax, University Physics Volume 1, Abschnitt 4.2: Beschleunigungsvektor.</a>

Durchschnittliche und momentane Geschwindigkeitsvektoren

Um andere physikalische Größen in der Kinematik zu berechnen, muss die Zeitvariable eingeführt werden. Die Zeitvariable ermöglicht es uns nicht nur anzugeben, wo ein Objekt ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Motion in Two or Three Dimensions

Bewegung in zwei oder drei Dimensionen

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 objects move continuously through space and time. Because of that, velocity at a single point along the path is also important. This is called instantaneous velocity, and it is often just called velocity. It is the average velocity between two points in the limit where the time interval, and therefore the displacement, approaches zero. Like average velocity, instantaneous velocity is a vector with units of length per time.

Position Change and Instant Velocity

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

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

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...

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 time, displacement, average velocity, and instantaneous velocity describe motion in kinematics. Clear high school physics support for grades 9–12.

Position Change and Instant Velocity | 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

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Forces And Motion

Motion

Motion Graphs

Virginia  Standards of Learning

HIgh School

PS.8

PS.8.a

PH.2

PH.2.a

PH.2.c

Texas Essential Knowledge and Skills

High School

PHYS.5

PHYS.5.D

Arizona Science Standards

HS+Phy.P3

HS+Phy.P3U1.3

Alabama Course of Study Science

Motion and Stability: Forces and Interactions

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

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 ...

Average Velocity

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

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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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To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object ...

Acceleration Vectors

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Direction of Acceleration Vectors

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Linear Momentum

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Force and Momentum

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Electrical Current

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Drift Velocity

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Current Density

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Resistivity

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Resistance

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Ohm's Law

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Non-ohmic Devices

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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

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Magnetic Fields

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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

The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). ...

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

Motion Of A Charged Particle In A Magnetic Field

A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move ...

Magnetic Force

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

magnetic-force-on-a-current-carrying-conductor

Magnetic Force On A Current-Carrying Conductor

Moving charges experience a force in a magnetic field. Since the magnetic fields produced by moving charges are proportional to the current, a conductor ...

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

Force On A Current Loop In A Magnetic Field

Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical ...

torque-on-a-current-loop-in-a-magnetic-field

Torque On A Current Loop In A Magnetic Field

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Consider a point charge moving with a ...

Biot-Savart Law

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magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

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Magnetic Field Of A Current Loop

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Divergence and Curl of Magnetic Field

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To evaluate the divergence of the ...

Ampere's Law

A fundamental property of a static magnetic field is that it is not conservative, unlike an electrostatic field. Instead, there is a relationship between ...

Ampere's Law: Problem-Solving

Ampere&#x27;s law states that for any closed looped path, the line integral of the magnetic field along the path equals the vacuum permeability times the ...

Solenoids

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field for a solenoid is the ...

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.

Position Change and Instant Velocity

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