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

The kinematic equations of motion are useful to solve problems involving one-dimensional&#160;motion of objects under constant acceleration.
Consider a couple driving to a nearby coffee shop. They start the car and apply a constant acceleration of 2 meters per second squared. What will be the car&#39;s velocity after 20 seconds and the distance covered by it in that time?
The choice of the equation to solve the problem depends on the known quantities and the unknown quantities.
Here, the known quantities are constant acceleration, time, the initial position, and the initial velocity, as the car was at rest. The unknown quantities are the velocity and distance covered after 20 seconds, which can be calculated using the first and second kinematic equations.
Substituting known values in the first kinematic equation gives the velocity of the car, which equals 40 meters per second.&#160;
Then, substituting the known values in the second kinematic equation, simplifying and solving it gives the distance covered by the car equal to 400 meters.

kinematische vergelijkingen: probleemoplossing

Bij het analyseren van ééndimensionale beweging met constante versnelling omvat de probleemoplossingsstrategie het identificeren van de bekende grootheden en het kiezen van de juiste kinematische vergelijkingen om de onbekenden op te lossen. Afhankelijk van de bekende en onbekende grootheden zijn één of twee kinematische vergelijkingen nodig. Over het algemeen is het aantal benodigde vergelijkingen gelijk aan het aantal onbekende grootheden in het gegeven voorbeeld. Bij tweepersoonsachtervolgingsproblemen moeten altijd twee vergelijkingen tegelijkertijd worden opgelost om de waarde van de onbekende te bepalen.

Bij complexe problemen is het niet altijd mogelijk om de onbekenden of de volgorde waarin ze moeten worden berekend direct te identificeren. In zulke scenario’s is het nuttig om een lijst van onbekenden op te stellen en een schets van het probleem te maken om de bewegingsrichting van een object te identificeren. Om het probleem op te lossen, worden de bekende grootheden samen met hun eenheden in de juiste vergelijking ingevuld. Deze stap levert een numeriek antwoord op en biedt tevens een controle op eenheden, wat kan helpen om fouten te vinden. Als de eenheden incorrect zijn, is er een fout gemaakt. Echter, correcte eenheden garanderen niet noodzakelijk dat het numerieke deel van het antwoord ook correct is.

De laatste stap bij het oplossen van problemen is controleren of het antwoord redelijk is. Deze laatste stap is cruciaal, aangezien het doel van de natuurkunde is om de natuur nauwkeurig te beschrijven. Om te controleren of het antwoord redelijk is, moet zowel de grootte als het teken van het antwoord worden geverifieerd, naast de eenheden. Dit helpt bij het verkrijgen van een conceptueel begrip van de problemen die worden opgelost. Soms kan een natuurkundig principe correct worden toegepast om een numeriek probleem op te lossen, maar toch een onredelijk resultaat opleveren.

Bijvoorbeeld, als een atleet een sprint begint met een versnelling van 0,4 m/s² gedurende 100 seconden, zou hun eindsnelheid 40 m/s (ongeveer 150 km/h) zijn. Dit resultaat is onrealistisch, aangezien een persoon niet gedurende 100 seconden met zo’n hoge snelheid kan rennen. Hier is de natuurkunde op zich correct, maar het beschrijven van de natuur gaat verder dan alleen het correct manipuleren van vergelijkingen.

Deze tekst is een bewerking van <a href="https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration">Openstax, University Physics Deel 1, Sectie 3.4: Beweging met constante versnelling</a>.

Kinematische vergelijkingen: probleemoplossing

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the ...

Education

JoVE Core

Natuurkunde

Unit 1

Onderdeel 1

Motion Along a Straight Line

Beweging langs een rechte lijn

KEY TERMS AND CONCEPTS

BELANGRIJKE TERMEN EN CONCEPTEN

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 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

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HIgh School

Physical Science

PS.8

PS.8.a

PH.2

PH.2.b

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HS.P3

HS.P3U1.6

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9-12.P.1.1.b

9-12.P.1.1.d

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SC.912.P.12

SC.912.P.12.2

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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

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

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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 ...

Kinematic Equations - II

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average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity 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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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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