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 vitesse instantanée peut être calculée à partir du graphique de position en fonction du temps. Supposons qu’un objet se déplace du point p1 au point p2. Ensuite, sa vitesse moyenne est donnée par la pente du graphique position-temps.
Ainsi, si le point p2 tend vers le point p1, et que la vitesse x moyenne est calculée sur des intervalles de temps plus courts de delta t, alors dans la limite où delta t tend vers zéro, la pente de la tangente à la courbe au point p1 représente le vecteur vitesse instantané.
Si la tangente à la courbe position-temps est ascendante ou descendante vers la droite, sa pente, sa vitesse x et son mouvement sont positifs ou négatifs en conséquence. 
Si la position en fonction du temps est connue, la vitesse instantanée à un instant donné peut être calculée.
En prenant la dérivée temporelle de la fonction de position, on estime le vecteur vitesse en fonction du temps. En substituant la valeur du temps, on peut obtenir la vitesse instantanée.

vélocité instantanée - ii

La vélocité instantanée est la grandeur qui mesure à quelle vitesse un objet se déplace le long de son trajet. En d'autres termes, la vélocité instantanée d'un objet est la limite de la vélocité moyenne lorsque le temps écoulé approche de zéro, ou la dérivée du déplacement par rapport au temps. Tout comme la vélocité moyenne, la vélocité instantanée est un vecteur avec des dimensions de longueur par unité de temps. La vélocité instantanée peut avoir des valeurs positives et négatives. La vélocité instantanée peut être calculée à partir du graphique temps-position. La vélocité instantanée à un moment spécifique est le taux de variation de la fonction de position, qui est la pente de la fonction de position à ce point. La pente de la tangente à n'importe quel point sur le graphique temps-position est égale à la vélocité à ce point. Une pente nulle indique que la vélocité instantanée est nulle. Une pente positive indique une vélocité instantanée positive, tandis qu'une pente négative indique une vélocité instantanée négative. Plus la pente est raide (positive ou négative), plus la vélocité de la particule est grande dans la direction positive ou négative.

Considérez le mouvement d'une particule dont la position est donnée par l'équation suivante :

<img alt="Equation1" src="/files/ftp_upload/12619/12619_Equation_1.png" style="text-align: center; height: 15px;" />

Que vaut la vélocité instantanée lorsque t = 0,25 s ?

Les quantités connues sont l'expression de la position en fonction du temps. Pour déterminer la vélocité instantanée, étudions d'abord l'équation suivante :

<img alt="Equation2" src="/files/ftp_upload/12619/12619_Equation_2.png" style="text-align: center; height: 30px;" />

En utilisant l'expression de x(t), l'expression de la vélocité est :

<img alt="Equation3" src="/files/ftp_upload/12619/12619_Equation_3.png" style="text-align: center; height: 10px;" />

En substituant la valeur du temps dans l'équation ci-dessus, la vélocité instantanée à 0,25 s est de 1,5 m/s.

Ce texte est adapté 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>

Vélocité instantanée - II

La vitesse instantanée est la quantité qui mesure la vitesse à laquelle un objet se déplace le long de sa trajectoire. En d’autres termes, la vitesse instantanée d’un objet ...

Education

Enseignement

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Physics

Physique

Unit 1

Unité 1

Motion Along a Straight Line

Mouvement rectiligne

KEY TERMS AND CONCEPTS

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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

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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...

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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...

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velocity-and-position-by-graphical-method

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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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Forces And Motion

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PS.8

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Motion and Stability: Forces and Interactions

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Analyze motion in terms of speed, velocity, acceleration, and momentum.

Instantaneous Velocity from Position Graphs

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