Name: constant-acceleration kinematics formulas
Uploaded: 2023-04-30T10:50:43.000Z
Duration: 1 min 18 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 - III

Zarówno pierwsze, jak i drugie równanie kinematyczne mają czas jako zmienną.
Trzecie równanie jest niezależne od czasu i obejmuje zależność między zmiennymi przemieszczeniem, prędkością x i stałym przyspieszeniem x.
Pierwsze równanie kinematyki jest przestawiane w celu uzyskania wyrażenia dla czasu. Co więcej, to wyrażenie czasowe jest podstawiane do drugiego równania kinematyki. Przesuń wyraz x0 w lewą stronę i pomnóż obie strony przez 2ax. Upraszczając go jeszcze bardziej, otrzymujemy wyrażenie na prędkość końcową podniesioną do kwadratu równą prędkości początkowej podniesionej do kwadratu plus dwukrotność przyspieszenia pomnożonego przez różnicę między odległością końcową a początkową. Jest to trzecie równanie kinematyczne.
Czwarte równanie kinematyczne nie obejmuje stałego przyspieszenia x i można je otrzymać, zrównując dwa wyrażenia dla średniej prędkości x wprowadzonej wcześniej. Obie strony są następnie mnożone przez czas t. Daje to zależność stwierdzającą, że różnica między odległością końcową a początkową jest równa średniej prędkości x w czasie początkowym i końcowym pomnożonej przez czas t.

równania kinematyczne - iii

W pierwszych dwóch równaniach kinematycznych zmienną jest czas, ale trzecie równanie kinematyczne jest niezależne od czasu. Równanie to wyraża prędkość końcową jako funkcję przyspieszenia i drogi, na której działa. Czwarte równanie kinematyczne nie ma składnika w postaci przyspieszenia i podaje końcowe położenie obiektu w chwili t w odniesieniu do prędkości początkowej i końcowej. Równanie to jest przydatne, gdy nie jest znana wartość stałego przyspieszenia.

Za pomocą równań kinematycznych można uzyskać opisowe informacje o ruchu obiektu. Proces opracowywania kinematyki zapewnia także wgląd w ogólne podejście do rozwiązywania problemów, które pozwala uzyskać zarówno prawidłowe odpowiedzi, jak i wgląd w zależności fizyczne. Te równania i powiązane strategie rozwiązywania problemów są pomocne tylko wtedy, gdy przyspieszenie jest stałe; jeśli przyspieszenie obiektu nie jest stałe, wymagane jest inne podejście do rozwiązania dynamiki obiektu.

Zastosowanie równań kinematycznych nie ogranicza się do ruchu jednowymiarowego. Równania te można uogólnić na wyższe wymiary, pod warunkiem, że przyspieszenie obiektu jest stałe. Podobnie równania te można również uogólnić na ruch obrotowy, używając odpowiednich wielkości fizycznych opisujących ruch obrotowy obiektu, o ile przyspieszenie kątowe obiektu jest stałe.

Ten tekst jest adaptacją <a href="https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant- przyspieszenie">Openstax, University Physics, tom 1, sekcja 3.4: Ruch ze stałym przyspieszeniem.</a>

Równania kinematyczne - III

Pierwsze dwa równania kinematyczne mają czas jako zmienną, ale trzecie równanie kinematyczne jest niezależne od czasu. Równanie to wyraża prędkość końcową ...

Education

JoVE Core

Fizyka

Unit 1

Jednostka 1

Motion Along a Straight Line

Ruch po linii prostej

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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 equation does not include acceleration. It gives the final position of an object at time t in terms of the initial and final velocities, so it is useful when the value of the constant acceleration is unknown.

These kinematic equations also show a general problem-solving method in physics. That method can lead to correct answers and to a better understanding of how physical quantities are related. The equations work only when acceleration is constant. If acceleration changes, a different approach is needed.

The same equations are not limited to motion in one straight line. They can be extended to motion in higher dimensions as long as acceleration remains constant. They can also be adapted for rotational motion by using quantities that describe rotation, provided the angular acceleration is constant.

Constant-Acceleration Kinematics Formulas

constant-acceleration-kinematics-formulas

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 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

Explore kinematic equations for constant acceleration, including time-free formulas, final velocity, final position, and extensions to higher and rotational motion.

Constant-Acceleration Kinematics Formulas | 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

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 ...

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

Kinematic Equations: Problem Solving

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Free-falling Bodies: Introduction

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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

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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

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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

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

Mass and weight are often used interchangeably in everyday conversation. For example,&#160; medical records often show our weight in kilograms, but never ...

Weightlessness

When an object is dropped, it accelerates toward the center of the Earth. If the net external force on the object is its weight, it is said to be in free ...

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

Newton&#39;s laws can be applied to bodies at rest and bodies in motion. Newton&#39;s first law is applied to bodies in equilibrium, whereas the second ...

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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 ...

Drag Force and Terminal Speed

An interesting force in everyday life is the force of drag on an object when it is moving in a fluid. Like friction, the drag force always opposes the ...

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Tension

Tension is a force along the length of a medium, in particular, a force carried by a flexible medium, such as a rope or cable. The word &#34;tension&#34; ...

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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.

Constant-Acceleration Kinematics Formulas

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