Creating And Using Kinematic Equations Chart - Kinematics - Physics

Summary

This video tutorial guides viewers on creating a kinematics equation chart, a valuable tool for solving kinematic problems. It outlines the five fundamental kinematic variables: displacement (Δx), initial velocity (VI), final velocity (VF), acceleration (a), and time (t). The video then presents four kinematic equations, each missing one of the variables, which is crucial for determining the appropriate equation to use based on the given and unknown variables in a problem. The tutorial demonstrates how to apply the chart to a real-world problem involving a car's acceleration and time to find the displacement, emphasizing the importance of identifying the unneeded variable to select the correct equation.

Takeaways

• 📚 The video teaches how to create a kinematics equation chart to solve kinematic problems.
• 🔢 Five key kinematic variables are identified: displacement (Δx), initial velocity (VI), final velocity (VF), acceleration (a), and time (t).
• 📈 Four fundamental kinematic equations are introduced: VF = VI + a*t, Δx = VI*t + 0.5*a*t^2, VF^2 = VI^2 + 2*a*Δx, and Δx = (VI + VF)*t/2.
• 🎨 The chart visually organizes equations by shading the variable that is not present in each equation, aiding in the selection of the appropriate equation for a given problem.
• 🔍 To use the chart, list the given and unknown variables in a problem, then identify the missing variable to select the correct equation.
• 🚗 An example problem is solved using the chart: finding the displacement of a car given initial velocity, acceleration, and time.
• 📝 The process involves writing down all variables, filling in the known values, and using the missing variable to pick the correct kinematic equation from the chart.
• 🧮 The example calculation demonstrates how to substitute the known values into the chosen equation to find the displacement.
• 📊 The kinematics chart is a tool to help quickly determine which equation to use based on the given and unknown variables in a problem.
• 💡 The video emphasizes the importance of recognizing the variable not needed for a problem to effectively use the kinematics chart.

Q & A

What are the five kinematic variables mentioned in the video?

The five kinematic variables mentioned are displacement (Δx), initial velocity (VI), final velocity (VF), acceleration (a), and time (t).

What are the four kinematic equations provided in the video?

The four kinematic equations are: 1) VF = VI + a*t, 2) Δx = VI*t + 0.5*a*t^2, 3) VF^2 = VI^2 + 2*a*Δx, and 4) Δx = (VI + VF)*t / 2.

How does the video suggest determining which kinematic equation to use for a problem?

The video suggests looking at the given and unknown variables in the problem and identifying the variable that is not needed (shaded in green in the kinematics chart) to determine which equation to use.

Why is it important to identify the variable that is not needed in a kinematic problem?

Identifying the variable that is not needed helps to determine which kinematic equation to use because the equation that does not contain that variable is the one that can be used to solve the problem.

What does the video demonstrate through the example of a car accelerating from an initial speed?

The video demonstrates how to use the kinematics chart to solve for displacement when given initial velocity, acceleration, and time, but not the final velocity.

How does the video explain the process of solving a kinematic problem using the chart?

The video explains the process by first writing down all the variables, filling in the given values, identifying the unknown variable, finding the corresponding equation on the chart that lacks the unknown variable, and then solving the equation.

What is the significance of shading the displacement variable in the first kinematic equation on the chart?

The displacement variable is shaded in the first kinematic equation on the chart to indicate that it is the variable not needed when using this equation, which helps in selecting the correct equation for a problem.

Why does the video emphasize the importance of the variable that is not asked for in a problem?

The variable that is not asked for in a problem is emphasized because it is the key to selecting the appropriate kinematic equation from the chart, as the chosen equation should not contain that variable.

What is the final result of the example problem involving a car accelerating for 5 seconds in the video?

The final result of the example problem is that the car travels a displacement of 62.5 meters in 5 seconds.

How does the video recommend verifying the correct kinematic equation for a given problem?

The video recommends verifying the correct kinematic equation by ensuring that the equation aligns with the given and unknown variables, specifically by confirming that the equation lacks the variable not needed for the problem.

Outlines

00:00

📚 Introduction to Kinematics Equation Chart

This paragraph introduces the concept of a kinematics equation chart, a tool designed to assist in solving kinematic problems by identifying the appropriate equation to use based on given and unknown variables. The paragraph outlines the five fundamental kinematic variables: displacement (Δx), initial velocity (VI), final velocity (VF), acceleration (a), and time (t). It then presents four kinematic equations: VF = VI + a*t, Δx = VI*t + 0.5*a*t^2, VF^2 = VI^2 + 2*a*Δx, and Δx = (VI + VF)*t/2. The process of determining which equation to use involves identifying the variable not present in the problem and using the corresponding equation where that variable is shaded out on the chart.

05:00

🔍 Applying the Kinematics Chart to a Problem

The second paragraph demonstrates the practical application of the kinematics chart by walking through a sample problem. The problem involves a car with an initial speed of 5 meters per second accelerating at 3 meters per second squared for 5 seconds, and the goal is to find the displacement. The paragraph explains how to identify the relevant equation by looking for the missing variable (VF in this case) and then using the corresponding equation where VF is shaded. The equation used is Δx = VI*t + 0.5*a*t^2. The paragraph concludes with the substitution of the given values into the equation, resulting in a displacement of 62.5 meters after performing the calculation.

Keywords

💡Kinematics

Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies without considering the causes of motion. In the context of the video, kinematics is the central theme, focusing on the development of equations to describe motion. The video aims to teach viewers how to create a kinematics equation chart to solve kinematic problems.

💡Kinematic Equations

Kinematic equations are mathematical formulas used to describe the motion of an object under constant acceleration. The video script provides four such equations: VF = VI + a · t, ΔX = VI · t + (1/2) a · t^2, VF^2 = VI^2 + 2a · ΔX, and ΔX = (1/2) (VI + VF) · t. These equations are essential for solving problems involving displacement, initial and final velocities, acceleration, and time.

💡Displacement (ΔX)

Displacement refers to the change in position of an object. It is a vector quantity that points from the initial to the final position. In the video, displacement is one of the five kinematic variables and is used in the kinematic equations to calculate how far an object has moved from its starting point.

💡Initial Velocity (VI)

Initial velocity is the speed of an object at the beginning of a time interval or at the start of a motion. The video mentions initial velocity as one of the variables in the kinematic equations, which is necessary to determine the motion of an object when acceleration and time are known.

💡Final Velocity (VF)

Final velocity is the speed of an object at the end of a time interval or motion. In the video, final velocity is highlighted as a variable that can be calculated using the kinematic equations when other variables like initial velocity, acceleration, and time are given.

💡Acceleration (a)

Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity that can be constant or variable. The video script includes acceleration as a key variable in the kinematic equations, which is used to determine how the velocity of an object changes over time.

💡Time (t)

Time is a measure in seconds of the duration of motion. In the video, time is one of the fundamental variables used in the kinematic equations to relate the changes in velocity and position of an object during its motion.

💡Variable

In the context of the video, a variable is a quantity that can change, such as displacement, initial velocity, final velocity, acceleration, and time. The video explains how to identify which kinematic equation to use based on the given and unknown variables in a problem.

💡Kinematics Equation Chart

The kinematics equation chart is a visual tool created in the video to help users determine which kinematic equation to use for a given problem. It involves shading the variable that is not needed (not given or not asked for) to solve the problem, which then points to the appropriate equation to use.

💡Given and Unknowns

In the video, 'given' refers to the known quantities provided in a problem, while 'unknowns' are the quantities that need to be calculated. The video script emphasizes the importance of identifying given and unknown variables to select the correct kinematic equation for solving motion problems.

💡Substitution

Substitution is a method used in the video to solve for an unknown variable by inserting the values of known variables into the chosen kinematic equation. The video demonstrates how to use substitution to calculate displacement when initial velocity, acceleration, and time are given.

Highlights

Introduction to creating a kinematics equation chart for solving kinematic problems.

Identification of five kinematic variables: displacement (ΔX), initial velocity (VI), final velocity (VF), acceleration (a), and time (t).

Listing of four fundamental kinematic equations.

Explanation of how to derive kinematic equations, with a reference to a previous video.

Step-by-step guide on analyzing which variables are present in each equation.

Visual method of shading the missing variable in each equation for easy identification.

Strategy for selecting the appropriate equation based on given and unknown variables in a problem.

Emphasis on the importance of identifying the variable not needed for the problem to choose the correct equation.

Example problem demonstrating the application of the kinematics chart.

Description of a car acceleration problem to illustrate the use of the kinematics chart.

Process of writing down all variables and filling them into the equation.

Identification of the second kinematic equation as the correct choice for the car problem.

Substitution of given values into the chosen kinematic equation.

Calculation of the car's displacement using the kinematic equation.

Final answer of 62.5 meters for the car's displacement after 5 seconds of acceleration.

Summary of the kinematic chart usage for solving kinematic problems.

Transcripts

in this video you will learn how to

create a kinematics equation chart this

will be very helpful for be able to

figure out which equation to use to

solve a particular kinematic equation

problem

first we're going to write down the five

kinematic

variables that you'll notice in these

problems so we have Delta X displacement

VI initial velocity VF final velocity a

acceleration and time

all right and then on the left hand side

we're going to write down the kinematic

equations so we have VF equals v i

plus a t

then we have Delta X

equals v i t plus one over two a t

squared

we have VF squared equals v i squared

plus 2A Delta X

and we have Delta x equals

one over two

v i plus VF

times T if you're wondering how we get

these equations you can look at my

previous video where I derive these four

kinematic equations

then the next step is to

think about what variables are in each

equation

so for the first one we have VI

we have VF we have acceleration we also

have time the one that we don't have is

the displacement so I'm going to go in

and I'm going to shade that in with my

green here okay because that's going to

be important

next I have my second kinematic equation

I have Delta X I have the displacement I

have an initial velocity at the

acceleration and I have time but what I

don't have

is the final velocity okay and we'll

come back to why this is important just

a moment we're going to fill this out

first and then next we have the third

kinematic equation and that has

displacement initial velocity final

velocity and acceleration but it doesn't

have the time

and then last one

we have

displacement initial velocity final

velocity and time but it doesn't have

the acceleration

okay so to figure out which equation to

use when you're solving a problem you're

going to look at the given and the

unknowns so you're going to write those

down

then you're going to use the variable

that's not needed to determine which

equation to use

this is the important part because the

variable that's not needed for the

problem is going to be the help us to

figure out which equation to use so

let's say for example that we were given

the initial velocity

we were given the final velocity and the

acceleration

and then we're looking for

the time so what equation would I what I

what I look would I use so what is

missing here is Delta X so if I look

through this equation I am missing Delta

X right so Delta X it's not in it's not

given it's not an unknown so for this

problem I would use the first kinematic

equation which is VF equals VI plus a t

Okay so depending on what is not given

and what is not not asked for it's not

the unknown

that is the variable you're going to

look for you're going to look for the

green shaded box and then that will tell

you which equation to use

so let's take a look at an actual

problem and try to apply our kinematics

chart so in this question it says a car

with initial speed of 5 meters per

second accelerates with 3 meters per

second squared how far does the car

travel in 5 seconds so what I like to do

first is to write down all my variables

I have Delta x v i v f

a and t okay and now I'm going to fill

them in so I know that the initial speed

is 5 meters per second I know it

accelerates at 3 meters per second

squared and the time uh the sorry the um

how we want to know how far in the time

that it travels for is five seconds okay

and we're looking for the displacement

how far does it travel

notice that the one variable that we

aren't given and we don't really care

about because they're not asking for it

is VF so I'm going to go to my chart I'm

going to look down VF and I'm going to

see that right there the f is shaded for

the second kinematic equation so that's

the equation I'm going to use so I'm

going to write that down and we'll have

Delta X

equals v i t plus 1 over 2 a t squared

now I wrote down the equation my next

step is the substitution so the I is 5

times T is five plus one over two

a is 3 and T is five so that's going to

be squared

5 times 5 is 25

times 3 times 5 squared that's

37.5 if I add that up I get 62.5 meters

and that's my displacement so once again

to use the kinematic chart you're going

to write down your given and your

unknown and whatever variable is left

over you're going to use that to find

that equation on the chart find words

highlighted and then use the equation on

the left side

thank you