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

Pierwsze równanie kinematyczne wyraża prędkość jako funkcję prędkości początkowej i zmiany prędkości.
Do wyprowadzenia drugiego równania kinematycznego stosuje się dwa równania średniej prędkości x w przedziale od t równym zeru do późniejszego czasu t. Pierwszym równaniem dla średniej prędkości x jest zmiana przemieszczenia w czasie zmiany, jak omówiono w poprzednich lekcjach. Tutaj pozycja początkowa jest oznaczona przez x0 w czasie t równym zero i x w późniejszym czasie t.
Zakładając, że przyspieszenie jest stałe, średnia prędkość x może być również przedstawiona jako średnia prędkości w czasie początkowym i końcowym. Podstawiając tutaj pierwsze równanie kinematyczne, otrzymujemy równanie położenia x w funkcji czasu.
Równanie to pokazuje, że położenie obiektu w dowolnym momencie t jest sumą jego położenia początkowego, odległości przebytej przy stałej prędkości początkowej oraz odległości przebytej podczas zmiany prędkości.

równania kinematyczne - ii

Drugie równanie kinematyczne wyraża końcowe położenie obiektu w kategoriach jego położenia początkowego, drogi przebytej ze stałą prędkością początkową oraz drogi przebytej w wyniku zmiany prędkości. Podobnie jak pierwsze równanie kinematyczne, to równanie jest również ważne tylko wtedy, gdy przyspieszenie jest stałe podczas całego ruchu obiektu.

Załóżmy, że samochód włącza się do ruchu autostradowego na rampie o długości 200 m. Jeżeli jego prędkość początkowa wynosi 10 m/s, a przyspiesza 2 m/s2, to czas, w jakim samochód przejedzie rampę o długości 200 m, można obliczyć korzystając z drugiego równania kinematycznego. Tutaj znane wielkości to odległość 200 m, prędkość początkowa samochodu 10 m/s i przyspieszenie 2 m/s2. Korzystając z drugiego równania kinematycznego

<img alt="Rysunek1" src="/files/ftp_upload/12623/12623_equation_1.png" style="text-align: center; height: 35px;" />

i podstawiając znane wielkości do powyższego równania, otrzymujemy

<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;" />

Użycie wzoru kwadratowego do obliczenia czasu daje dwa rozwiązania: t = 10 s i t = µ20 s. Ujemna wartość czasu jest nieuzasadniona, ponieważ oznaczałaby, że zdarzenie miało miejsce 20 s przed rozpoczęciem ruchu, dlatego możemy odrzucić to rozwiązanie. Zatem czas potrzebny samochodowi na przejechanie rampy o długości 200 m wynosi 10 s.

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 - II

Drugie równanie kinematyczne wyraża końcowe położenie obiektu pod względem jego położenia początkowego, odległości przebytej z początkową stałą ...

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

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...

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

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

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

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

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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

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Average Acceleration

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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 ...

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

Position and Displacement Vectors

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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

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Newton's First Law: Application

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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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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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