Name: velocity from constant acceleration
Uploaded: 2023-04-30T10:50:28.000Z
Duration: 1 min 26 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 - I

우리 주변에서 우리는 속도 변화율이 운동 전체에 걸쳐 동일한 일정한 가속도로 움직이는 물체의 많은 예를 볼 수 있습니다. 예를 들어, 중력 아래에서 떨어지는 공은 공기의 영향을 무시하면 일정한 가속도를 갖습니다.
일정한 가속도를 가진 물체의 움직임은 운동 방정식(equation of motion)이라고도 하는 운동학 방정식(kinematic equations)에 의해 근사화됩니다. 이러한 방정식에는 변위, 속도, 가속도 및 시간과 같은 변수가 포함됩니다.
가속도는 시간에 따른 속도의 변화라는 것을 기억하십시오. 이제 물체가 초기 속도 v0x로 0 초와 같은 시간 t1에서 움직이기 시작하고 t 초와 같은 시간 t2 가 최종 속도 vx를 갖는다고 가정합니다.
이러한 변수를 대체한 후 가속도와 시간의 곱은 시간 t에 따른 속도의 총 변화에 해당합니다. 따라서 언제든지 t 의 x 속도는 초기 속도와 x 속도의 변화의 합으로 주어집니다. vx에 대한 이 표현식은 첫 번째 기본 운동학 방정식입니다.

운동 방정식 - i

물체가 일정한 가속도로 움직일 때, 물체의 속도는 움직이는 내내 일정한 속도로 변합니다. 물체의 가속도가 일정한 경우에 대해 운동의 운동 방정식이 도출됩니다. 첫 번째 운동 방정식은 속도, 가속도 및 시간 간의 관계에 대한 통찰력을 제공합니다. 예를 들어 다음과 같습니다.

<ol style="list-style-type: circle;">
	<li>최종 속도는 가속도의 크기와 지속 시간에 따라 달라집니다.</li>
	<li>가속도가 0이면 최종 속도는 예상대로 초기 속도와 같습니다(즉, 속도는 일정합니다)</li>
	<li>가속도가 음수이면 최종 속도는 초기 속도보다 작습니다.</li>
</ol>

이 모든 관찰은 우리의 직관에 부합합니다. 우리의 직관과 경험에 비추어 기본 방정식을 검토하여 자연을 정확하게 설명하는지 확인하는 것이 항상 도움이 된다는 점에 유의하세요.

초기 속도 70m/s로 착륙하고 40초 동안 1.5m/s2로 감속하는 비행기를 생각해 보세요. 그런 다음 첫 번째 운동 방정식을 사용하여 비행기의 최종 속도를 계산할 수 있습니다. 알려진 양은 초기 속도, 일정한 (감속) 가속도 및 시간입니다. 방정식에 알려진 값을 대입하면

<img alt="그림1" src="/files/ftp_upload/12622/12622_equation_1.png" style="text-align: center; height: 15px;" />

<img alt="Figure2" src="/files/ftp_upload/12622/12622_equation_2.png" style="text-align: center; height: 18px;" />

비행기의 최종 속도는 10m/s입니다.

이 텍스트는 <a href="https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-에서 수정되었습니다. 가속도">Openstax, 대학 물리학 1권, 섹션 3.4: 일정한 가속도를 갖는 모션.</a>

운동 방정식 - I

물체가 일정한 가속도로 움직일 때 물체의 속도는 동작 전반에 걸쳐 일정한 비율로 변합니다. 의 운동학 방정식 ...

Education

교육

JoVE Core

물리학

Unit 1

제1단원

Motion Along a Straight Line

직선 운동

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 acceleration is negative, the final velocity is smaller than the initial velocity. These results show why it is useful to check equations against everyday intuition.

A plane landing gives a clear example. If an airplane starts at 70 m/s and slows down at 1.5 m/s^2 for 40 seconds, the first kinematic equation can be used to find the final velocity. Using the initial velocity, the constant deceleration, and the time, the final velocity is 10 m/s. This example shows how the equation can predict motion in a real situation.

Velocity from Constant Acceleration

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 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 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

Learn how the first kinematic equation links initial velocity, constant acceleration, and time, with a plane landing example and simple motion results.

Velocity from Constant Acceleration | 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

Virginia  Standards of Learning

HIgh School

Physical Science

PS.8

PS.8.a

PH.2

PH.2.b

Arizona Science Standards

High School

HS.P3

HS.P3U1.6

Alabama Course of Study Science

Motion and Stability: Forces and Interactions

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

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PS.Phy.1.2

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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

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Newton's First Law: Application

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Internal and External Forces

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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.

Velocity from Constant Acceleration

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