Name: average velocity and average speed
Uploaded: 2023-04-30T10:49:50.000Z
Duration: 1 min 12 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

Average Velocity

The average velocity tells how fast an object is moving over time and is defined as the total displacement between two points divided by the time taken to travel between them.
For example, if p1 and p2 are the positions of an object at time t1 and t2, then average x-velocity is given as <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;">&#916;x divided by <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;">&#916;t. Note that the average velocity is a vector quantity and could be positive or negative depending on whether the displacement is positive or negative.
The position versus time graph is a pictorial way to represent how an object changes position with time. It plots the time on the x-axis and the position on the y-axis. Therefore, the average x velocity of the object equals the slope of the line p1, p2.
Average speed is defined as the total distance traveled by a body divided by the time taken to complete the distance. Unlike average velocity, it is a scalar quantity.

gemiddelde snelheid

Om de andere fysische grootheden in de kinematica te berekenen, moeten we de tijdsvariabele introduceren. De tijdsvariabele stelt ons niet alleen in staat om de positie van het object tijdens zijn beweging te bepalen, maar ook hoe snel het beweegt. De snelheid waarmee een object beweegt, wordt gegeven door de snelheid waarmee de positie verandert in de tijd. Voor elke positie xi wijzen we een specifieke tijd ti toe.

Als de details van de beweging op elk moment niet belangrijk zijn, wordt de snelheid meestal uitgedrukt als de gemiddelde snelheid. Deze vectoriële grootheid is eenvoudigweg de totale verplaatsing tussen twee punten Δx, gedeeld door de tijd die nodig is om ertussen te reizen, Δt. De gemiddelde snelheid is een vector en kan positief of negatief zijn, afhankelijk van de begin- en eindpositie. De uitdrukking voor de gemiddelde snelheid is gegeven door:

<img alt="Equation1" src="/files/ftp_upload/12617/12617_Equation_1.png" style="height: 35px;">

De gemiddelde snelheid moet niet worden verward met de gemiddelde snelheidsschaal (average speed), die wordt berekend als de totale afgelegde afstand gedeeld door de verstreken tijd. Dit is niet noodzakelijk gelijk aan de grootte van de gemiddelde snelheid.

Bijvoorbeeld, als een reis begint en eindigt op dezelfde locatie, is de totale verplaatsing nul, en is de gemiddelde snelheid dus nul. De gemiddelde snelheidsschaal is echter niet nul, omdat de totale afgelegde afstand groter is dan nul.

Als we een autorit maken van 300 km en we op een bepaald tijdstip op onze bestemming moeten zijn, dan zijn we geïnteresseerd in de gemiddelde snelheidsschaal. De kilometerteller van een auto meet de totale afgelegde afstand. De totale afstand afgelegd door de auto gedeeld door de totale tijd geeft de gemiddelde snelheidsschaal van de auto.

Bijvoorbeeld, de Shanghai Maglev-trein verbindt Longyang Road met Pudong International Airport, een afstand van 30 km. De reis duurt gemiddeld 8 minuten.

De bekende grootheden zijn de afstand en tijd. De onbekende grootheid, de gemiddelde snelheid, is de totale afstand gedeeld door de tijd.

Deze tekst is een bewerking van <a href="https://openstax.org/books/university-physics-volume-1/pages/3-1-position-displacement-and-average-velocity">Openstax, University Physics Volume 1, Sectie 3.1: Positie, verplaatsing en gemiddelde snelheid</a>.

Gemiddelde snelheid

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 ...

Education

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Physics

Natuurkunde

Unit 1

Onderdeel 1

Motion Along a Straight Line

Beweging langs een rechte lijn

KEY TERMS AND CONCEPTS

BELANGRIJKE TERMEN EN CONCEPTEN

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

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 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

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

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Ohio’s Learning Standards and Model Curriculum

Forces And Motion

Motion

Problem Solving

Virginia  Standards of Learning

HIgh School

PS.8

PS.8.a

PH.2

PH.2.a

Arizona Science Standards

High School

HS.P3

HS.P3U1.6

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

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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Instantaneous Velocity - II

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average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

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PS.PSc.6.2

Continuity Equation

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PS.PSc.6.3

Magnetism

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Magnetic Field Lines

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Magnetic Flux

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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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Magnetic Force On A Current-Carrying Conductor

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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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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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