Name: velocity from constant acceleration
Uploaded: 2023-04-30T10:50:28.000Z
Duration: 1 min 26 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

Physics

motion-and-stability-forces-and-interactions

Motion and Stability- Forces and Interactions

PS.Phy.1.1

Kinematic Equations - I

Um uns herum sehen wir viele Beispiele von Objekten, die sich mit konstanter Beschleunigung bewegen, wobei die Änderungsrate der Geschwindigkeit während der gesamten Bewegung gleich ist. Zum Beispiel hat eine Kugel, die unter der Schwerkraft fällt, eine konstante Beschleunigung, wenn die Auswirkungen der Luft vernachlässigt werden.
Die Bewegung von Objekten mit konstanter Beschleunigung wird durch kinematische Gleichungen, auch Bewegungsgleichungen genannt, approximiert. Diese Gleichungen enthalten Variablen wie Verschiebung, Geschwindigkeit, Beschleunigung und Zeit.
Erinnern Sie sich daran, dass Beschleunigung die Änderung der Geschwindigkeit mit der Zeit ist. Nehmen wir nun an, dass sich ein Objekt zum Zeitpunkt t1 gleich null Sekunden mit einer Anfangsgeschwindigkeit v0x zu bewegen beginnt, und nach einiger Zeit t2 gleich t Sekunden hat es eine Endgeschwindigkeit vx.
Nach der Substitution dieser Variablen entspricht das Produkt aus Beschleunigung und Zeit der Gesamtänderung der Geschwindigkeit über die Zeit t. Somit ist die x-Geschwindigkeit zu jedem Zeitpunkt t gegeben durch die Summe der Anfangsgeschwindigkeit und der Änderung der x-Geschwindigkeit. Dieser Ausdruck für vx ist die erste grundlegende kinematische Gleichung.

kinematische gleichungen - i

Wenn ein Objekt mit konstanter Beschleunigung bewegt wird, ändert sich die Geschwindigkeit des Objekts während der Bewegung mit einer konstanten Rate. Die kinematischen Gleichungen der Bewegungen werden für solche Fälle abgeleitet, in denen die Beschleunigung des Objekts konstant ist. Die erste kinematische Gleichung gibt Einblick in die Beziehung zwischen Geschwindigkeit, Beschleunigung und Zeit. Wir können beispielsweise sehen:

<ol style="list-style-type: disc;">
	<li>Die Endgeschwindigkeit hängt davon ab, wie groß die Beschleunigung ist und wie lange sie dauert.</li>
	<li>Wenn die Beschleunigung null ist, entspricht die Endgeschwindigkeit der Anfangsgeschwindigkeit, wie erwartet (mit anderen Worten, die Geschwindigkeit ist konstant).</li>
	<li>Wenn die Beschleunigung negativ ist, ist die Endgeschwindigkeit kleiner als die Anfangsgeschwindigkeit.</li>
</ol>

All diese Beobachtungen passen zu unserer Intuition. Beachten Sie, dass es immer hilfreich ist, die grundlegenden Gleichungen im Hinblick auf unsere Intuition und Erfahrung zu überprüfen, um sicherzustellen, dass sie die Natur genau beschreiben.

Betrachten Sie ein Flugzeug, das mit einer Anfangsgeschwindigkeit von 70 m/s landet und sich über 40 Sekunden mit einer Verringerung der Geschwindigkeit von 1,5 m/s² verlangsamt. Dann kann die Endgeschwindigkeit des Flugzeugs mithilfe der ersten kinematischen Gleichung berechnet werden. Die bekannten Größen sind Anfangsgeschwindigkeit, konstante Verlangsamung/Beschleunigung und Zeit. Durch Einsetzen der bekannten Werte in die Gleichung ergibt sich:

<img alt="Figure1" src="/files/ftp_upload/12622/12622_equation_1.png" style="text-align: center; height: 15px;" />

<img alt="Figure2" src="/files/ftp_upload/12622/12622_equation_2.png" style="text-align: center; height: 18px;" />

Die Endgeschwindigkeit des Flugzeugs beträgt 10 m/s.

Dieser Text ist angepasst von <a href="https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration">Openstax, University Physics Volume 1, Abschnitt 3.4: Bewegung mit konstanter Beschleunigung.</a>

Kinematische Gleichungen - I

Wenn sich ein Objekt mit konstanter Beschleunigung bewegt, ändert sich die Geschwindigkeit des Objekts während der gesamten Bewegung mit einer konstanten Geschwindigkeit. Die kinematischen Gleichungen von ...

Education

Lehre

JoVE Core

Physik

Unit 1

Einheit 1

Motion Along a Straight Line

Bewegung entlang einer Geraden

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 acceleration is negative, the final velocity is smaller than the initial velocity. These results show why it is useful to check equations against everyday intuition.

A plane landing gives a clear example. If an airplane starts at 70 m/s and slows down at 1.5 m/s^2 for 40 seconds, the first kinematic equation can be used to find the final velocity. Using the initial velocity, the constant deceleration, and the time, the final velocity is 10 m/s. This example shows how the equation can predict motion in a real situation.

Velocity from Constant Acceleration

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 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 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 the first kinematic equation links initial velocity, constant acceleration, and time, with a plane landing example and simple motion results.

Velocity from Constant Acceleration | 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.

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Ohio’s Learning Standards and Model Curriculum

Motion

Problem Solving

Virginia  Standards of Learning

HIgh School

Physical Science

PS.8

PS.8.a

PH.2

PH.2.b

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.b

9-12.P.1.1.d

Florida Department of Education

SC.912.P.12

SC.912.P.12.2

Texas Essential Knowledge and Skills

PHYS.5

PHYS.5.C

Georgia Standards of Excellence

SP1.

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PS.Phy.2.1

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PS.Phy.2.2

Analyze the motion of objects using time, distance, displacement, speed, velocity, and acceleration.

Velocity from Constant Acceleration

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