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

La velocidad instantánea se puede calcular a partir del gráfico de posición frente al tiempo. Supongamos que un objeto se mueve del punto p1 al punto p2. Luego, su velocidad promedio viene dada por la pendiente del gráfico de posición-tiempo.
Por lo tanto, si el punto p2 se aproxima al punto p1, y la velocidad x promedio se calcula en intervalos de tiempo más cortos de delta t, entonces en el límite cuando delta t tiende a cero, la pendiente de la tangente a la curva en el punto p1 representa la velocidad instantánea.
Si la tangente a la curva posición-tiempo tiene una pendiente ascendente o descendente hacia la derecha, su pendiente, velocidad x y movimiento son positivos o negativos en consecuencia. 
Si se conoce la posición en función del tiempo, se puede calcular la velocidad instantánea en un momento dado.
Tomando la derivada del tiempo de la función de posición, se estima la velocidad en función del tiempo. Sustituyendo el valor del tiempo, se puede obtener la velocidad instantánea.

velocidad instantánea - ii

La velocidad instantánea es la magnitud que mide cómo de rápido se mueve un objeto a lo largo de su trayectoria. En otras palabras, la velocidad instantánea de un objeto es el límite de la velocidad promedio cuando el tiempo transcurrido se acerca a cero, o la derivada de la posición con respecto al tiempo. Al igual que la velocidad promedio, la velocidad instantánea es un vector con dimensiones de longitud por unidad de tiempo. La velocidad instantánea puede tener tanto valores positivos como negativos. La velocidad instantánea se puede calcular a partir del gráfico posición-tiempo. La velocidad instantánea en un momento específico es la tasa de cambio de la función de posición, que es la pendiente de la función de posición en ese punto. La pendiente de la tangente en cualquier punto del gráfico posición-tiempo es igual a la velocidad en ese punto. Una pendiente cero indica que la velocidad instantánea es cero. Una pendiente positiva indica una velocidad instantánea positiva, mientras que una pendiente negativa indica una velocidad instantánea negativa. Cuanto más pronunciada sea la pendiente (positiva o negativa), mayor será la velocidad de la partícula en dirección positiva o negativa. Considera el movimiento de una partícula en la cual la posición se encuentra dada por <img alt="Equation1" src="/files/ftp_upload/12619/12619_Equation_1.png" style="text-align: center; height: 15px;"> ¿Cuál es la velocidad instantánea en t = 0,25 s? Las cantidades conocidas son la expresión de la posición como función del tiempo. Para determinar la velocidad instantánea, primero considera la ecuación <img alt="Equation2" src="/files/ftp_upload/12619/12619_Equation_2.png" style="text-align: center; height: 30px;"> Utilizando la expresión de x(t), la expresión para la velocidad es <img alt="Equation3" src="/files/ftp_upload/12619/12619_Equation_3.png" style="text-align: center; height: 10px;"> Sustituyendo el valor del tiempo en la ecuación anterior, la velocidad instantánea a los 0,25 s es 1,5 m/s. Este texto está adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/3-2-instantaneous-velocity-and-speed">Openstax, University Physics Volume 1, Section 3.2: Instantaneous Velocity and Speed.</a>

Velocidad Instantánea - II

La velocidad instantánea es la cantidad que mide la rapidez con la que un objeto se mueve a lo largo de su trayectoria. En otras palabras, la velocidad instantánea de un objeto ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Motion Along a Straight Line

Movimiento en línea recta

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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 Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

PS.Phy.1.1

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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

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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

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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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Acceleration Vectors

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Direction of Acceleration Vectors

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Linear Momentum

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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

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

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

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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

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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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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

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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.

Instantaneous Velocity from Position Graphs

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