Name: instantaneous velocity from position graphs
Uploaded: 2023-04-30T10:50:05.000Z
Duration: 1 min 10 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

Instantaneous Velocity - II

يمكن حساب السرعة اللحظية من الرسم البياني للموضع مقابل الوقت. لنفترض أن كائنا يتحرك من النقطة p1 إلى النقطة p2. ثم يتم إعطاء متوسط سرعته من خلال ميل الرسم البياني للموضع والوقت.
لذلك ، إذا اقتربت النقطة p2 من النقطة p1 ، وتم حساب متوسط السرعة x على فترات زمنية أقصر من دلتا t ، فعندئذ في الحد حيث تميل دلتا t إلى الصفر ، يمثل ميل المماس إلى المنحنى عند النقطة p1 السرعة اللحظية.
إذا كان ظل منحنى الموضع والوقت ينحدر لأعلى أو لأسفل إلى اليمين ، فإن ميله وسرعة x وحركته تكون موجبة أو سالبة وفقا لذلك. 
إذا كان الموضع كدالة للوقت معروفا ، فيمكن حساب السرعة اللحظية في أي وقت.
بأخذ مشتق الوقت لوظيفة الموضع ، يتم تقدير السرعة كدالة للوقت. باستبدال قيمة الوقت ، يمكن الحصول على السرعة اللحظية.

السرعة المتجهة اللحظية - ii

<div style="direction:rtl">السرعة المتجهة اللحظية هي الكمية التي تقيس مدى سرعة تحرك الجسم على طول مساره. بمعنى آخر، السرعة المتجهة اللحظية لجسم ما هي الحد الأقصى لمتوسط السرعة المتجهة عندما يقترب الزمن المنقضي من الصفر، أو مشتقة الإزاحة بالنسبة للزمن. مثل السرعة المتجهة المتوسطة، فإن السرعة المتجهة اللحظية عبارة عن متجه له أبعاد الطول لكل وحدة زمنية. يمكن أن يكون للسرعة المتجهة اللحظية قيم موجبة وسالبة. يمكن حساب السرعة المتجهة اللحظية من الرسم البياني للموضع -الزمن. السرعة المتجهة اللحظية عند نقطة زمنية محددة هي معدل تغير دالة الموضع، وهو ميل دالة الموضع عند تلك النقطة. ميل المماس عند أي نقطة على الرسم البياني للموضع -الزمن يساوي السرعة المتجهة عند تلك النقطة. يشير الميل الصفري إلى أن السرعة المتجهة اللحظية تساوي صفرًا. ويشير الميل الموجب إلى السرعة المتجهة اللحظية موجبة، في حين يشير الميل السالب إلى السرعة المتجهة اللحظية السالبة . كلما كان الميل أكثر انحدارًا (موجباً أو سالباً)، زادت سرعة الجسيم في الاتجاه الموجب أو السالب. فكر في حركة الجسيم الذي يتم تحديد موضعه بواسطة <img alt="Equation1" src="/files/ftp_upload/12619/12619_Equation_1.png" style="text-align: center; height: 15px;"> ما هي السرعة المتجهة اللحظية عند t = 0.25 s؟ الكميات المعروفة هي تعبير الموضع كدالة في الزمن. لتحديد السرعة المتجهة اللحظية، عليك أولًا النظر في المعادلة <img alt="Equation2" src="/files/ftp_upload/12619/12619_Equation_2.png" style="text-align: center; height: 30px;"> باستخدام تعبير x(t)، يكون تعبير السرعة المتجهة هو <img alt="Equation3" src="/files/ftp_upload/12619/12619_Equation_3.png" style="text-align: center; height: 10px;"> بالتعويض عن قيمة الزمن ، في المعادلة أعلاه، تكون السرعة المتجهة اللحظية عند 0.25 ثانية هي 1.5 م/ث. هذا النص مقتبس من <a href="https://openstax.org/books/university-physics-volume-1/pages/3-2-instantaneous-velocity-and-speed">Openstax، الفيزياء الجامعية المجلد 1، القسم 3.2: السرعة المتجهة اللحظية والسرعة.</a></div>

السرعة المتجهة اللحظية - II

السرعة اللحظية هي الكمية التي تقيس مدى سرعة تحرك الجسم على طول مساره. بمعنى آخر ، السرعة اللحظية لجسم ما ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

Motion Along a Straight Line

الحركة في خط مستقيم

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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 curve. The instantaneous velocity at one time point is the rate of change of the position function. It is also the slope of the tangent line at that point on the graph.

The sign of the slope tells the direction of motion. A zero slope means the instantaneous velocity is zero. A positive slope means positive instantaneous velocity. A negative slope means negative instantaneous velocity. The steeper the slope, the greater the particle’s speed in the positive or negative direction.

To find an instant velocity from a position function, use the expression for position as a function of time. First, write the equation for x(t). Then find the velocity expression from it. For a particle with a given position function, substituting t = 0.25 s gives an instantaneous velocity of 1.5 m/s. This approach matches the definition used for position-time graphs and changing motion.

Instantaneous Velocity from Position Graphs

instantaneous-velocity-from-position-graphs

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

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 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 instantaneous velocity comes from a position-time graph, tangent slope, and the derivative of position, with a sample value at t = 0.25 s.

Instantaneous Velocity from Position Graphs | 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.1.1

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

Alabama Course of Study Science

Motion and Stability: Forces and Interactions

9-12.P.1.1

9-12.P.1.1.a

Florida Department of Education

High School

SC.912.P.12

SC.912.P.12.2

Texas Essential Knowledge and Skills

PHYS.5

PHYS.5.A

PHYS.5.C

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 ...

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

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 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

The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic ...

Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position ...

average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

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

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Direction of Acceleration Vectors

Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the direction ...

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

Force and momentum are intimately related. Force acting over time can change momentum, and Newton&#39;s second law of motion can be stated in its most ...

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

Electrical Current

Electrical current is defined as the rate at which charge flows. When there is a large current present, such as that used to run a refrigerator, a large ...

Drift Velocity

The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance. Thus, when a free charge is forced ...

Current Density

The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, ...

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

Many materials exhibit a simple relationship between the values of current, voltage, and resistance, known as Ohm&#8217;s law. The current that flows ...

Non-ohmic Devices

In most substances, the current flow is proportional to the voltage applied to it. A simple relationship between the values of current, voltage, and ...

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

PS.PSc.6.2

Continuity Equation

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area ...

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current ...

Electrical Conductivity

In perfect conductors, the electric field inside is always zero due to the abundance of free electrons, which nullify any field by flowing. As a result, ...

Theory of Metallic Conduction

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the ...

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

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

In a magnetic field, moving charges encounter a force. If a wire contains these moving charges, i.e., if the wire is carrying a current, then a force acts ...

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

The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between ...

The Hall Effect

Edwin H. Hall, in the year 1879, devised an experiment that could be used to identify the polarity of the predominant charge carriers in a conducting ...

Magnetic Field due to Moving Charges

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a ...

Biot-Savart Law

The Biot-Savart law gives the magnitude and direction of the magnetic field produced by a current. This empirical law was named in honor of two ...

Biot-Savart Law: Problem-Solving

The magnitude and direction of a magnetic field created by a steady current can be calculated using the Biot-Savart law.
Consider a mobile phone battery ...

Magnetic Field Due to Two Straight Wires

Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the ...

magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

Two long, straight, and parallel current-carrying conductors exert a force of equal magnitude on one another. The direction of the force depends on the ...

Magnetic Field Of A Current Loop

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the ...

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot&#8211;Savart Law can be expressed as follows:

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 ...

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.

Instantaneous Velocity from Position Graphs

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