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

As equações cinemáticas de movimento são úteis para resolver problemas envolvendo movimento unidimensional de objetos sob aceleração constante.
Considere um casal dirigindo para uma cafeteria próxima. Eles ligam o carro e aplicam uma aceleração constante de 2 metros por segundo ao quadrado. Qual será a velocidade do carro após 20 segundos e a distância percorrida por ele nesse tempo?
A escolha da equação para resolver o problema depende das quantidades conhecidas e das quantidades desconhecidas.
Aqui, as quantidades conhecidas são aceleração constante, tempo, posição inicial e velocidade inicial, pois o carro estava em repouso. As quantidades desconhecidas são a velocidade e a distância percorridas após 20 segundos, que podem ser calculadas usando a primeira e a segunda equações cinemáticas.
A substituição de valores conhecidos na primeira equação cinemática fornece a velocidade do carro, que é igual a 40 metros por segundo. 
Então, substituindo os valores conhecidos na segunda equação cinemática, simplificando-a e resolvendo-a, obtém-se a distância percorrida pelo carro igual a 400 metros.

equações cinemáticas: resolução de problemas

Quando analisamos o movimento unidimensional com aceleração constante, a estratégia para resolver problemas envolve identificar as quantidades conhecidas e escolher as equações cinemáticas apropriadas para calcular as incógnitas. Podem ser necessárias uma ou duas equações cinemáticas para calcular as incógnitas, dependendo das quantidades conhecidas e desconhecidas. Geralmente, o número de equações necessárias é igual ao número de incógnitas no exemplo dado. Problemas de movimento com dois corpos sempre requerem duas equações, a serem resolvidas simultaneamente para determinar o valor das incógnitas.

Em problemas complexos, nem sempre é possível identificar as incógnitas ou a ordem em que elas devem ser calculadas. Nesses cenários, é útil fazer uma lista das incógnitas e desenhar um esboço do problema para identificar as direções de movimento de um objeto. Para resolver o problema, substitua os valores conhecidos, juntamente com suas unidades, na equação apropriada. Essa etapa fornece uma resposta numérica e também serve como verificação das unidades, o que ajuda a identificar erros. Se as unidades estiverem incorretas, um erro foi cometido. No entanto, unidades corretas não garantem necessariamente que a parte numérica da resposta também esteja correta.

A etapa final na resolução de problemas é verificar se a resposta é razoável. Essa etapa final é crucial, pois o objetivo da física é descrever a natureza de maneira precisa. Para verificar se a resposta é razoável, verifique tanto sua magnitude quanto seu sinal, além de suas unidades. Isso nos permite obter uma compreensão conceitual dos problemas que estão sendo resolvidos. Às vezes, o princípio físico pode ser aplicado corretamente para resolver um problema numérico, mas produz um resultado irracional. Por exemplo, se um atleta acelerar a 0,4 m/s² por 100 segundos em uma corrida a pé, sua velocidade final será de 40 m/s (cerca de 150 km/h). Esse resultado é irracional porque uma pessoa não pode correr a essa velocidade tão alta por 100 segundos. Aqui, a física está correta em certo sentido, mas descrever a natureza envolve mais do que apenas manipular as equações corretamente.

Este texto foi adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration">Openstax, University Physics Volume 1, Section 3.4: Motion with Constant Acceleration</a>.

Equações cinemáticas: resolução de problemas

Ao analisar o movimento unidimensional com aceleração constante, a estratégia de resolução de problemas envolve a identificação das grandezas conhecidas e a escolha do ...

Education

JoVE Core

Física

Unit 1

Unidade 1

Motion Along a Straight Line

Movimento Retilíneo

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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 - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

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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

All objects, neglecting air resistance, fall with the same acceleration towards the Earth&#39;s center due to the force exerted by the Earth&#39;s ...

Free-falling Bodies: Example

An object falling without any air resistance under the influence of gravitational force is said to be in free-fall. For free-falling bodies, the ...

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

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Direction of Acceleration Vectors

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Projectile Motion

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/files/media/science-education/science-education-thumbs/12634.jpg

Projectile Motion: Equations

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Projectile Motion: Example

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principle-linear-impulse-momentum-for-single-particle-problem

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

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Non-uniform Circular Motion

In&#160;uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all ...

Relative Velocity in One Dimension

The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a ...

Relative Velocity in Two Dimensions

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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

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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

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Weightlessness

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Apparent Weight

True weight is the measure of the gravitational force acting on an object. However, if the object accelerates, its measured weight is different from its ...

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Newton's Third Law: Introduction

Whenever one body exerts a force on a second body, the first body experiences a force equal in magnitude and opposite in direction, to the force that it ...

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

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Drag Force and Terminal Speed

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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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