Name: average velocity and average speed
Uploaded: 2023-04-30T10:49:50.000Z
Duration: 1 min 12 s
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North Carolina K-12 Science Standard Course of Study

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Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.4.1

Average Velocity

Le vecteur vitesse moyen indique la vitesse à laquelle un objet se déplace au fil du temps et est défini comme le déplacement total entre deux points divisé par le temps nécessaire pour se déplacer entre eux.
Par exemple, si p1 et p2 sont les positions d’un objet à l’instant t1 et t2, alors la vitesse x moyenne est donnée comme suit : <span style="taille-police : 11pt ; famille-police : Arial ; couleur : rgb(0, 0, 0) ; couleur-arrière-plan : transparent ; font-variant-numeric : normal ; font-variant-east-asian : normal ; vertical-align : baseline ; white-space : pre-wrap ;">Δx divisé par <span style="font-size : 11pt ; font-family : Arial ; color : rgb(0, 0, 0) ; background-color : transparent ; font-variant-numeric : normal ; font-variant-east-asian : normal ; vertical-align : baseline ; white-space : pre-wrap ;">Δt. Notez que le vecteur vitesse moyen est une grandeur vectorielle et peut être positif ou négatif selon que le déplacement est positif ou négatif.
Le graphique de la position en fonction du temps est une façon illustrée de représenter comment un objet change de position avec le temps. Il trace le temps sur l’axe des x et la position sur l’axe des y. Par conséquent, le vecteur vitesse x moyen de l’objet est égal à la pente de la droite p1, p2.
La vitesse moyenne est définie comme la distance totale parcourue par un corps divisée par le temps nécessaire pour parcourir la distance. Contrairement à la vitesse moyenne, il s’agit d’une grandeur scalaire.

vitesse moyenne

Pour calculer les autres grandeurs physiques en cinématique, nous devons introduire la variable temps. La variable temps nous permet non seulement de décrire la position de l'objet pendant son mouvement, mais aussi sa vitesse. La vitesse à laquelle un objet se déplace est donnée par le taux de changement de position par rapport au temps. Pour chaque position xi, nous attribuons un temps particulier ti. Si les détails du mouvement à chaque instant ne sont pas importants, le taux de changement est généralement exprimé sous la forme de la vitesse moyenne. Cette quantité vectorielle est simplement le déplacement total entre deux points, Δx, divisé par le temps mis pour les parcourir, Δt. La vitesse moyenne est un vecteur et peut être une valeur positive ou négative, en fonction des positions initiale et finale. L'expression de la vitesse moyenne est donnée par :

Vitesse moyenne = Δx/Δt

La vitesse moyenne, quant à elle, est la distance totale parcourue divisée par le temps écoulé, et n'est pas nécessairement la même que la magnitude de la vélocité moyenne. Par exemple, si un voyage commence et se termine au même endroit, le déplacement total est nul et donc la vélocité moyenne est nulle. Cependant, la vitesse moyenne n'est pas nulle, car la distance totale parcourue est supérieure à zéro. Si nous faisons un voyage en voiture de 300 km et devons arriver à notre destination à une certaine heure, alors nous serions intéressés par notre vitesse moyenne. L'odomètre d'une voiture mesure la distance totale parcourue. Donc, la distance totale parcourue par la voiture divisée par le temps total donne la vitesse moyenne de la voiture.

Par exemple, le Maglev, le train à sustentation magnétique de Shanghai relie Longyang Road à l'aéroport international de Pudong, qui est à une distance de 30 km. Le trajet prend en moyenne 8 minutes. Quelle est la vitesse moyenne du train à sustentation magnétique ?

Les quantités connues sont la distance et le temps. La quantité inconnue, la vitesse moyenne, est la distance totale divisée par le temps. Ainsi, la vitesse moyenne du train à sustentation magnétique est de 225 km/h.

Ce texte est adapté de <a href="https://openstax.org/books/university-physics-volume-1/pages/3-1-position-displacement-and-average-velocity">Openstax, University Physics Volume 1, Section 3.1: Position, Displacement, and Average Velocity</a>.

Vitesse moyenne

Pour calculer les autres grandeurs physiques en cinématique, nous devons introduire la variable temps. La variable temps nous permet non seulement d’énoncer la position ...

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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 interval, Δt.

Because it is a vector, average velocity can be positive or negative. The sign depends on the object’s initial and final positions. Average speed is different. It is the total distance traveled divided by the elapsed time, so it is not necessarily the same as the magnitude of average velocity.

A round trip shows the difference clearly. If an object starts and ends at the same place, its total displacement is zero, so its average velocity is zero. Its average speed is not zero, because the total distance traveled is still greater than zero. On a road trip of 300 km, average speed is the quantity that matters if you need to reach a destination by a certain time. A car’s odometer measures total distance traveled, so dividing that distance by total time gives the car’s average speed.

The Shanghai Maglev train gives another example. It travels from Longyang Road to Pudong International Airport over a distance of 30 km. The trip takes about 8 minutes on average. Using the distance and time, the train’s average velocity is 225 km/hr.

Average Velocity and Average Speed

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 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 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...

average acceleration

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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...

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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...

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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

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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

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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 average velocity and average speed are calculated from displacement, distance, and time, with simple motion examples for high school physics.

Average Velocity and Average Speed | JoVE K12

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Describing Motion

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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.

Average Velocity and Average Speed

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