Name: using the second kinematic equation
Uploaded: 2025-05-22T09:05:40.000Z
Duration: 1 min 17 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 - II

La première équation cinématique exprime le vecteur vitesse en fonction du vecteur vitesse initial et de la variation du vecteur vitesse.
Pour calculer la deuxième équation cinématique, deux équations pour la vitesse moyenne x sont utilisées pendant un intervalle de t égal à zéro à un temps ultérieur t. La première équation de la vitesse moyenne x est la variation du déplacement au cours de la variation du temps, comme nous l’avons vu dans les leçons précédentes. Ici, la position initiale est notée x0 à l’instant t égal à zéro et x à l’instant t ultérieur.
En supposant que l’accélération est constante , le vecteur vitesse x moyen peut également être représenté comme la moyenne des vitesses aux temps initial et final. En substituant ici la première équation cinématique, on obtient une équation pour la position x en fonction du temps.
Cette équation montre que la position d’un objet à n’importe quel instant t est la somme de sa position initiale, de la distance parcourue sous une vitesse initiale constante et de la distance parcourue lors du changement de vitesse.

Équations cinématiques - ii

La deuxième équation cinématique exprime la position finale d'un objet en fonction de sa position initiale, de la distance parcourue avec une vélocité constante initiale et de la distance parcourue en raison d'un changement de vélocité. Tout comme la première équation cinématique, cette équation n'est également valable que lorsque l'accélération est constante pendant le mouvement d'un objet.

Supposons qu'une voiture s'insère dans la circulation sur une voie de 200 m de long. Si sa vélocité initiale est de 10 m/s et qu'elle accélère à 2 m/s2, alors le temps pris par la voiture pour parcourir la rampe de 200 m peut être calculé en utilisant la deuxième équation cinématique. Ici, les quantités connues sont la distance de 200 m, la vélocité initiale de la voiture de 10 m/s et l'accélération de 2 m/s2. En utilisant la deuxième équation cinématique

<img alt="Figure1" src="/files/ftp_upload/12623/12623_equation_1.png" style="text-align: center; height: 35px;" />

et en substituant les quantités connues dans l'équation ci-dessus, nous obtenons

<img alt="Figure2" src="/files/ftp_upload/12623/12623_equation_2.png" style="text-align: center; height: 35px;" />

<img alt="Figure3" src="/files/ftp_upload/12623/12623_equation_3.png" style="text-align: center; height: 15px;" />

En utilisant la formule quadratique pour résoudre l'équation du temps, nous obtenons deux solutions : t = 10 s et t = -20 s. Une valeur négative pour le temps est insensée, car cela signifierait que l'événement s'est produit 20 s avant le début du mouvement, nous pouvons donc ignorer cette solution. Ainsi, le temps pris par la voiture pour parcourir la rampe de 200 m est de 10 s.

Ce texte est adapté 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>

Équations cinématiques - II

La deuxième équation cinématique exprime la position finale d’un objet en fonction de sa position initiale, de la distance parcourue avec la constante initiale ...

Education

Enseignement

JoVE Core

Physique

Unit 1

Unité 1

Motion Along a Straight Line

Mouvement rectiligne

KEY TERMS AND CONCEPTS

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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 velocity, and the acceleration, so the second kinematic equation can be used to find the time.

Substituting the values into the equation leads to a quadratic equation for time. Solving it gives two answers: t = 10 s and t = −20 s. The negative time is not reasonable, because it would mean the motion happened 20 s before it started, so that solution is discarded. The time for the car to travel the 200 m ramp is 10 s.

Using the Second Kinematic Equation

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...

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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

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...

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velocity and position by graphical method

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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

Use the second kinematic equation to solve constant-acceleration motion problems. Follow a car on a 200 m ramp and find the travel time step by step.

Using the Second Kinematic Equation | JoVE K12

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JoVE Core Physique présente plusieurs branches de la physique fondamentale grâce à des vidéos animées concises et faciles à comprendre ; cela inclut: la cinématique, la dynamique, la mécanique des fluides, la mécanique statique, les ondes et l'acoustique. En parallèle, les vidéos de scientifiques à l'action démontrent l'application de concepts associés à ces domaines dans des expériences de recherche classiques et originales réalisées dans des laboratoires modernes du monde entier.

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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

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HIgh School

Physical Science

PS.8

PS.8.a

PH.2

PH.2.b

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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

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kinematic-equations-for-one-dimensional-motion

Kinematic Equations for One-Dimensional Motion

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Instantaneous Acceleration

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Kinematic Equations - I

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

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PS.Phy.1.2

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PS.Phy.2.1

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Newton's First Law: Application

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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.

Using the Second Kinematic Equation

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