Name: solving constant acceleration motion problems
Uploaded: 2023-04-30T10:50:50.000Z
Duration: 1 min 15 s
Channel: JoVE

K12 Standards

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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: Problem Solving

Die kinematischen Bewegungsgleichungen sind nützlich, um Probleme zu lösen, bei denen es um die eindimensionale Bewegung von Objekten unter konstanter Beschleunigung geht.
Stellen Sie sich vor, ein Paar fährt zu einem nahe gelegenen Café. Sie starten das Auto und wenden eine konstante Beschleunigung von 2 Metern pro Sekunde zum Quadrat an. Wie hoch ist die Geschwindigkeit des Autos nach 20 Sekunden und die Strecke, die es in dieser Zeit zurücklegt?
Die Wahl der Gleichung zur Lösung des Problems hängt von den bekannten Größen und den unbekannten Größen ab.
Hier sind die bekannten Größen die konstante Beschleunigung, die Zeit, die Anfangsposition und die Anfangsgeschwindigkeit, da sich das Auto im Ruhezustand befand. Bei den unbekannten Größen handelt es sich um die nach 20 Sekunden zurückgelegte Geschwindigkeit und die zurückgelegte Strecke, die mit Hilfe der ersten und zweiten kinematischen Gleichung berechnet werden können.
Wenn man bekannte Werte in der ersten kinematischen Gleichung einsetzt, erhält man die Geschwindigkeit des Autos, die 40 Metern pro Sekunde entspricht. 
Wenn man dann die bekannten Werte in der zweiten kinematischen Gleichung einsetzt, vereinfacht und löst, erhält man die vom Auto zurückgelegte Strecke von 400 Metern.

kinematische gleichungen: problemlösung

Bei der Analyse eindimensionaler Bewegung mit konstanter Beschleunigung besteht die Problemlösungsstrategie darin, die bekannten Größen zu identifizieren und die passenden kinematischen Gleichungen zur Lösung der Unbekannten auszuwählen. Je nach den bekannten und unbekannten Größen werden entweder eine oder zwei kinematische Gleichungen benötigt. Im Allgemeinen entspricht die Anzahl der erforderlichen Gleichungen der Anzahl der unbekannten Größen im gegebenen Beispiel. Für Probleme mit der Verfolgung von zwei Körpern sind immer zwei Gleichungen erforderlich, um den Wert der Unbekannten abzuleiten.

In komplexen Problemen ist es nicht immer möglich, die Unbekannten oder die Reihenfolge, in der sie berechnet werden sollten, zu identifizieren. In solchen Szenarien ist es nützlich, eine Liste der Unbekannten zu erstellen und eine Skizze des Problems anzufertigen, um die Bewegungsrichtungen eines Objekts zu identifizieren. Um das Problem zu lösen, setzen Sie die bekannten Größen zusammen mit ihren Einheiten in die entsprechende Gleichung ein. Dieser Schritt liefert eine numerische Antwort und dient auch als Überprüfung der Einheiten, die dabei helfen können, Fehler zu finden. Wenn die Einheiten falsch sind, wurde ein Fehler gemacht. Richtig eingestellte Einheiten garantieren jedoch nicht unbedingt, dass der numerische Teil der Antwort ebenfalls korrekt ist.

Der letzte Schritt zur Problemlösung besteht darin, die Antwort zu überprüfen, um festzustellen, ob sie vernünftig ist. Dieser letzte Schritt ist entscheidend, da das Ziel der Physik darin besteht, die Natur genau zu beschreiben. Um festzustellen, ob die Antwort vernünftig ist, überprüfen Sie sowohl ihren Betrag als auch ihr Vorzeichen sowie ihre Einheiten. Dadurch erhalten wir ein konzeptionelles Verständnis der gelösten Probleme. Manchmal kann das physikalische Prinzip richtig angewendet werden, um das numerische Problem zu lösen, führt jedoch zu einem unvernünftigen Ergebnis. Wenn zum Beispiel ein Athlet bei einem Wettlauf 0,4 m/s² beschleunigt und dies 100 Sekunden lang macht, wird seine Endgeschwindigkeit 40 m/s betragen (ca. 150 km/h). Dieses Ergebnis ist unvernünftig, da eine Person nicht 100 Sekunden lang mit einer so hohen Geschwindigkeit laufen kann. Hier ist die Physik in gewisser Weise korrekt, aber das Beschreiben der Natur geht weit über das bloße Manipulieren von Gleichungen hinaus.

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: Problemlösung

Bei der Analyse einer eindimensionalen Bewegung mit konstanter Beschleunigung besteht die Problemlösungsstrategie darin, die bekannten Größen zu identifizieren und die ...

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

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 require two equations solved at the same time to find the unknown value.

For more complex problems, it may not be easy to see the unknowns or the order for finding them. In that case, it helps to make a list of unknown quantities and draw a sketch of the situation. The sketch can show the direction of motion for each object and make the setup clearer.

After choosing the equation, substitute the known values with their units. This gives a numerical answer and also checks the units. If the units do not work out, an error has been made. Correct units do not always mean the number is correct, so the result still needs a final check.

The last step is to decide whether the answer is reasonable. Check the size of the value, its sign, and its units. This matters because physics aims to describe nature accurately. For example, if an athlete starts a foot race and accelerates at 0.4 m/s^2 for 100 seconds, the final speed would be 40 m/s, or about 150 km/h. That answer is not realistic for a person, even if the equation was used correctly.

Solving Constant Acceleration Motion Problems

solving-constant-acceleration-motion-problems

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

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 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 to solve one-dimensional constant acceleration problems using kinematic equations, unit checks, sketches, and reasonableness checks.

Solving Constant Acceleration Motion Problems | 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

Tennessee Academic Standards

High School

Motion and Stability: Forces and Interactions

PHYS.PS2.2

Virginia  Standards of Learning

HIgh School

Physical Science

PS.8

PS.8.a

PH.2

PH.2.b

Arizona Science Standards

HS.P3

HS.P3U1.6

Alabama Course of Study Science

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.

kinematic-equations-for-one-dimensional-motion

Kinematic Equations for One-Dimensional Motion

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

Average Velocity

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 ...

Instantaneous Velocity - I

The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To ...

Instantaneous Velocity - II

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object ...

Average Acceleration

The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic ...

Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

Kinematic Equations - I

When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of ...

Kinematic Equations - II

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant ...

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity ...

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the ...

Free-falling Bodies: Introduction

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Free-falling Bodies: Example

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Velocity and Position by Graphical Method

Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph ...

Velocity and Position by Integral Method

If acceleration as a function of time is known, then velocity and position functions can be derived using integral calculus. For constant acceleration, ...

Use models (graphs, equations, diagrams) to infer motion in one dimension.

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position ...

average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object ...

Acceleration Vectors

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Direction of Acceleration Vectors

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Projectile Motion

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Projectile Motion: Equations

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Projectile Motion: Example

The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to throw ...

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Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

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Non-uniform Circular Motion

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Relative Velocity in One Dimension

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Relative Velocity in Two Dimensions

Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to ...

Use models (graphs, equations, diagrams) to infer motion in two dimensions.

PS.Phy.1.2

Force

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Types of Forces

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Drawing Free-body Diagrams: Rules

The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams are useful in ...

Free Body Diagrams: Examples

Solving problems that involve forces is easy using free-body diagrams. A free-body diagram is a sketch showing all the external forces that are acting on ...

Use free body models to qualitatively and quantitatively analyze systems of forces in one dimension and two dimensions.

PS.Phy.2.1

Newton's First Law: Introduction

Motion draws our attention. Motion itself can be beautiful, causing us to marvel at the forces needed to create spectacular sights, such as that of a ...

Newton's First Law: Application

Experience suggests that an object at rest remains at rest if left alone, and that an object in motion tends to slow down and stop unless some effort is ...

Internal and External Forces

Newton&#39;s first law states that a net external force causes a change in motion. External forces act on an object or system, originating outside of the ...

Newton's Second Law

Newton&#39;s second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes ...

Mass and Weight

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Weightlessness

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Apparent Weight

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Newton's Third Law: Introduction

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Newton's Third Law: Examples

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first-law-particles-in-one-dimensional-equilibrium

First Law: Particles in One-dimensional Equilibrium

Newton&#39;s first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a ...

first-law-particles-in-two-dimensional-equilibrium

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic ...

Second Law: Motion under Same Force

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Second Law: Motion under Same Acceleration

Newton&#39;s second law of motion applies to bodies moving under the same acceleration. For example, when a baggage tractor pulls luggage carts, each cart ...

Carry out investigations to explain the interactions of forces on an object according to Newton's Laws of Motion.

PS.Phy.2.2

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

Solving Constant Acceleration Motion Problems

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