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

K12 Standards

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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 velocità istantanea può essere calcolata dal grafico della posizione rispetto al tempo. Supponiamo che un oggetto si sposti dal punto p1 al punto p2. Quindi la sua velocità media è data dalla pendenza del grafico posizione-tempo.
Quindi, se il punto p2 si avvicina al punto p1 e la velocità x media viene calcolata su intervalli di tempo più brevi del delta t, allora nel limite in cui il delta t tende a zero, la pendenza della tangente alla curva nel punto p1 rappresenta la velocità istantanea.
Se la tangente alla curva posizione-tempo si inclina verso l'alto o verso il basso verso destra, la pendenza, la velocità x e il movimento sono positivi o negativi di conseguenza. 
Se la posizione in funzione del tempo è nota, è possibile calcolare la velocità istantanea in un dato momento.
Prendendo la derivata temporale della funzione di posizione, viene stimata la velocità in funzione del tempo. Sostituendo il valore del tempo, si può ottenere la velocità istantanea.

velocità istantanea – ii

La velocità istantanea è la grandezza che misura quanto velocemente si muove un oggetto in un percorso. In altre parole, la velocità istantanea di un oggetto è il limite della velocità media quando il tempo trascorso si avvicina a zero o la derivata dello spostamento rispetto al tempo. Come la velocità media, la velocità istantanea è un vettore avente dimensioni di lunghezza per unità di tempo. La velocità istantanea può avere valori sia positivi che negativi. Essa può essere calcolata usando il grafico posizione-tempo. La velocità istantanea in uno specifico lasso di tempo è la velocità di cambiamento della funzione di posizione, che è l'inclinazione della funzione di posizione in quel punto. Un'inclinazione uguale a zero indica che la velocità istantanea è zero. Un'inclinazione positiva indica una velocità istantanea positiva, mentre una negativa indica una velocità istantanea negativa. Più ripida è la pendenza (positiva o negativa), e maggiore sarà la velocità della particella in una direzione positiva o negativa.

Considera il moto di una particella la cui posizione è data da:

<img alt="Equation1" src="/files/ftp_upload/12619/12619_Equation_1.png" style="text-align: center; height: 15px;" />

Qual è la velocità istantanea se t = 0,25 s?

Le grandezze conosciute sono l'espressione della posizione in funzione del tempo. Per determinare la velocità istantanea, per prima cosa, considera l'equazione:

<img alt="Equation2" src="/files/ftp_upload/12619/12619_Equation_2.png" style="text-align: center; height: 30px;" />

Usando l'espressione x(t) la velocità è:

<img alt="Equation3" src="/files/ftp_upload/12619/12619_Equation_3.png" style="text-align: center; height: 10px;" />

Sostituendo il valore per il tempo, nell'equazione precedente, la velocità istantanea a 0,25s è uguale a 1,5 m/s

Questo testo è stato tratto e adattato da <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>

Velocità istantanea – II

La velocità istantanea è la quantità che misura la velocità con cui un oggetto si muove lungo il suo percorso. In altre parole, la velocità istantanea di un oggetto ...

Education

Didattica

JoVE Core

Physics

Fisica

Unit 1

Unità 1

Motion Along a Straight Line

Moto rettilineo

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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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

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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

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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.

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Ohio’s Learning Standards and Model Curriculum

Forces And Motion

Motion

Motion Graphs

Virginia  Standards of Learning

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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

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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

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Average Velocity

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average-and-instantaneous-velocity-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

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

Motion Of A Charged Particle In A Magnetic Field

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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.

Instantaneous Velocity from Position Graphs

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