Kinematics Part 1: Horizontal Motion

Summary

Professor Dave introduces the concept of horizontal motion in classical physics, focusing on kinematics, which describes motion without considering forces. He explains that kinematics, developed by Galileo, uses equations to predict the motion of objects in one and two dimensions. The video covers three fundamental kinematic equations involving displacement, velocity, acceleration, and time, and demonstrates their application to real-world examples, such as calculating velocity and distance traveled for a car accelerating from rest and stopping from a given velocity. The summary emphasizes the simplicity and universality of these equations, applicable to all objects on Earth and in space, and invites viewers to subscribe for more educational content.

Takeaways

• 📚 Classical physics is divided into kinematics and dynamics, focusing on the motion of objects without and with forces, respectively.
• 🌟 Kinematics was largely developed by Galileo in the early 1600s, breaking away from Aristotle's view of imperfect earthly motion.
• 🔢 Kinematic equations involve variables for displacement, velocity, acceleration, and time, with constant acceleration in this context.
• 📉 Subscript 'zero' after velocity or displacement indicates initial conditions, which are crucial for solving problems.
• ⚙️ The three fundamental kinematic equations relate velocity, position, and acceleration to time and initial conditions.
• 🚗 Additional equations help define average velocity and position in terms of time intervals and final/initial velocities.
• 🛣️ Real-world examples, such as driving to the supermarket, demonstrate how to apply kinematic equations to find velocity and distance traveled.
• 🏎️ For a car accelerating from rest, velocity after time 't' can be found by multiplying acceleration by time, and distance by using the kinematic equation for position.
• 🚑 In the case of braking, the time to stop and the braking distance can be calculated using the same set of kinematic equations.
• 🔁 The kinematic equations are universally applicable to any object in motion, not just cars.
• 📈 Understanding and applying these equations allows for the prediction of motion under various conditions, showcasing the power of classical mechanics.

Q & A

What are the two main branches of mechanics in classical physics?

The two main branches of mechanics in classical physics are kinematics and dynamics.

Who is credited with largely developing kinematics?

Galileo is credited with largely developing kinematics in the early 1600s.

What is the primary focus of kinematics?

Kinematics focuses on equations that describe the motion of objects without reference to forces of any kind.

How does dynamics differ from kinematics?

Dynamics is the study of the effect that forces have on the motion of objects, unlike kinematics which does not consider forces.

What was the common belief about mathematical descriptions of motion before Galileo?

Before Galileo, it was believed that mathematics could only describe the perfect motion of divine celestial objects and that the motion of objects on earth was too imperfect and unpredictable to calculate.

What are the variables included in the kinematic equations?

The kinematic equations include variables for displacement, velocity, acceleration, and time.

Why is acceleration considered to have a constant value in kinematics?

In kinematics, acceleration is considered to have a constant value because the study does not look at forces that could cause acceleration to change over time.

What does the subscript of zero after velocity or displacement indicate?

The subscript of zero after velocity or displacement indicates initial conditions, which have implications depending on the problem being analyzed.

What are the three fundamental kinematic equations mentioned in the script?

The three fundamental kinematic equations are: 1) velocity at any time T is equal to initial velocity plus acceleration times time, 2) position with respect to a point of origin is equal to initial position plus initial velocity times time plus one-half the acceleration times time squared, and 3) velocity squared is equal to initial velocity squared plus twice the acceleration times displacement.

What are the two supplemental equations derived from simple definitions in kinematics?

The two supplemental equations are: position is equal to the average velocity times the time interval, and the average velocity is equal to final velocity plus initial velocity over 2.

How can the kinematic equations be applied to calculate the velocity and distance traveled by a car accelerating at a constant rate?

The kinematic equations can be applied by plugging in known values such as initial velocity, acceleration, and time to calculate the final velocity and distance traveled. For example, if a car starts from rest and accelerates at 2.5 m/s² for 10 seconds, its velocity would be 25 m/s and it would have traveled 125 meters.

How can you determine the time it takes for a moving car to stop and the distance it travels while braking?

You can determine the time it takes for a car to stop by using the equation that relates final velocity, initial velocity, and acceleration. Once you have the time, you can use another equation to find the braking distance by plugging in the initial velocity, acceleration, and time.

How does the script demonstrate the universality of kinematic equations?

The script demonstrates the universality of kinematic equations by showing that they can be applied to any object, not just cars, and that they govern the motion of all objects whether on earth or in space.

Outlines

00:00

📚 Introduction to Mechanics and Kinematics

Professor Dave introduces the concept of horizontal motion within the realm of classical physics, specifically focusing on mechanics. Mechanics is divided into kinematics and dynamics. Kinematics, which originated from Galileo's work in the 1600s, deals with the motion of objects without considering forces, while dynamics examines the effects of forces on motion. The tutorial series will concentrate on kinematics, exploring equations that govern motion in one and two dimensions. It highlights a historical shift from Aristotle's belief that mathematics could only describe celestial motions to Galileo's discovery that the same principles apply to earthly objects, albeit with the need for approximations due to variables like friction and atmosphere. The kinematic equations involve variables such as displacement, velocity, acceleration, and time, with constant acceleration values. Initial conditions are denoted by a subscript of zero. The fundamental kinematic equations are presented, relating velocity, position, and acceleration to time and displacement. Supplemental equations are also introduced, derived from definitions of average velocity and position. The equations are then applied to real-world examples, such as driving to the supermarket with a constant acceleration, to demonstrate how to calculate velocity and distance traveled.

05:02

🚗 Applying Kinematic Equations to Real-World Motion

This paragraph delves into applying the kinematic equations to calculate the velocity and distance of a car after a certain time with a given constant acceleration. It provides a step-by-step guide on using the equations to find the car's velocity after 10 seconds and the distance it would have traveled. The example illustrates the process of plugging in known values into the equations to solve for unknowns. The paragraph then shifts to a scenario where a car in motion needs to stop quickly, using deceleration. It explains how to use the kinematic equations to determine the time it takes for the car to stop and the braking distance. The process involves solving for time first, using the final velocity (which is zero in this case), initial velocity, and acceleration. Once the time is known, another equation is used to find the distance traveled during braking. The paragraph concludes by emphasizing that these kinematic equations are universally applicable to any object, not just cars, and encourages viewers to subscribe for more tutorials and support the content creation.

Keywords

💡Classical Physics

Classical Physics refers to the branch of physics that deals with the study of the motion of objects and the forces that affect them without considering quantum effects or relativity. In the context of the video, classical physics is the overarching subject, with a focus on mechanics, which is a subset that includes both kinematics and dynamics. The script discusses how classical physics revolutionized our understanding of motion, moving away from Aristotle's ideas to Galileo's mathematical descriptions.

💡Mechanics

Mechanics is a fundamental area of physics that studies the behavior of physical bodies when subjected to forces or displacements. It is divided into kinematics and dynamics. In the video, mechanics is the central theme, with kinematics being the focus of the tutorials. The script explains that mechanics is essential for understanding how simple equations govern the motion of objects in one and two dimensions.

💡Kinematics

Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion. It was largely developed by Galileo in the early 1600s. The video emphasizes kinematics as it deals with the equations that describe motion, such as displacement, velocity, acceleration, and time, without reference to the forces causing the motion.

💡Dynamics

Dynamics is the other branch of mechanics that studies the effect of forces on the motion of objects. While the video's primary focus is on kinematics, dynamics is mentioned as a counterpart to kinematics within the realm of mechanics. The script contrasts kinematics with dynamics by stating that dynamics involves the study of forces' effects on motion.

💡Displacement

Displacement is a vector quantity that refers to the change in position of an object. It is one of the variables included in the kinematic equations discussed in the video. The script uses displacement in the context of the second kinematic equation to describe the position of an object with respect to a point of origin after a certain time and acceleration.

💡Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. The video script introduces the concept of velocity in the context of the first kinematic equation, stating that the velocity of an object at any time is equal to the initial velocity plus the product of acceleration and time.

💡Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. In kinematics, as discussed in the video, acceleration is assumed to have a constant value. The script provides examples of how acceleration is used in the kinematic equations to calculate velocity and displacement.

💡Time

Time is a scalar quantity that represents the duration between two events. In the video, time is a critical variable in the kinematic equations, used to calculate changes in velocity and displacement. The script illustrates the role of time in determining the motion of objects, such as calculating the velocity of a car after 10 seconds of acceleration.

💡Kinematic Equations

Kinematic equations are mathematical formulas used to describe the motion of objects in terms of displacement, velocity, acceleration, and time. The video provides three fundamental kinematic equations and two supplemental equations that are used to solve problems related to motion. These equations are central to the video's theme of understanding motion without considering the forces involved.

💡Constant Acceleration

Constant acceleration refers to the situation where an object's acceleration does not change over time. In the context of the video, constant acceleration is a key assumption in kinematics, allowing for the use of simple equations to describe motion. The script gives examples of problems involving constant acceleration, such as a car accelerating at a rate of 2.5 meters per second squared.

💡Initial Conditions

Initial conditions are the starting values for variables such as velocity and displacement at the beginning of a motion scenario. The video script mentions that when a subscript of zero is used after velocity or displacement, it indicates initial conditions. These conditions are crucial for solving kinematic problems, as they provide the baseline from which changes are measured.

💡Deceleration

Deceleration is the decrease in the velocity of an object, which can be caused by an applied force in the opposite direction of motion. In the video, deceleration is used in the context of a car that needs to stop suddenly, with a rapid deceleration of -8.4 meters per second squared. The script uses deceleration to illustrate how the kinematic equations can be applied to calculate the time and distance required for a car to come to a stop.

💡Average Velocity

Average velocity is defined as the total displacement divided by the total time taken for that displacement. The video script introduces the concept of average velocity and provides a supplemental equation that relates average velocity to the initial and final velocities. This concept is used to solve problems involving the position of an object over a time interval.

Highlights

Classical physics focuses on mechanics, which is divided into kinematics and dynamics.

Kinematics, developed by Galileo in the early 1600s, describes motion without reference to forces.

Dynamics studies the effect that forces have on the motion of objects.

Galileo's work revolutionized the understanding that mathematics can describe all motion, celestial or terrestrial.

Kinematic equations include variables for displacement, velocity, acceleration, and time.

In kinematics, acceleration is assumed to have a constant value.

Subscript of zero after velocity or displacement indicates initial conditions.

Three fundamental kinematic equations govern the motion of objects in one and two dimensions.

The equations are derived from definitions of average velocity and position.

Real-world examples are used to apply kinematic equations, such as driving to the supermarket.

Initial velocity, acceleration, and time can be used to calculate velocity and distance traveled.

A constant acceleration of 2.5 m/s² results in a velocity of 25 m/s after 10 seconds.

The distance traveled can be calculated using the formula: 1/2 * acceleration * time².

For a car in motion with a velocity of 27 m/s, rapid deceleration can be modeled to find stopping time and distance.

A deceleration of -8.4 m/s² results in a stopping time of 3.2 seconds.

The braking distance can be calculated using the initial velocity, deceleration, and time.

Kinematic equations are universally applicable to any object, not just cars.

The tutorial encourages viewers to subscribe for more content and support the channel on Patreon.

Transcripts

It's professor Dave, let's talk about

horizontal motion.

As we learn classical physics, a big topic of

study will be mechanics. This is a branch

of physics that can be divided into two

smaller topics: kinematics and dynamics.

Kinematics, which was developed largely

by Galileo in the early 1600s, deals with

equations that describe the motion of

objects without reference to forces of

any kind,

whereas dynamics is the study of the

effect that forces have on the motion of

objects. These topics together comprise

mechanics. We are going to focus on

kinematics over the next few tutorials

so that we can familiarize ourselves

with the ways that simple equations will

govern the motion of objects in one and

two dimensions. These equations are

revolutionary, because from Aristotle

until Galileo we thought that mathematics

could only describe the perfect motion

of divine celestial objects, and that the

motion of objects on earth was too

imperfect and unpredictable to calculate.

But we soon found that the same

equations governing the motion of all

objects, whether on earth or in space, it

is simply that on earth we must make

approximations since there are a greater

number of variables like friction and

atmosphere that affect motion in various

ways. The kinematic equations include

variables for displacement, velocity,

acceleration, and time, and in the context

of kinematics acceleration will always

have a constant value, whether positive,

negative, or zero, since we won't look at

forces that could cause acceleration to

change over time. When you see a

subscript of zero after velocity or

displacement it indicates initial

conditions which will have some

implication depending on the problem we

are looking at. Here are the three

fundamental kinematic equations we will

be using. The first one says that the

velocity of an object at any time T is

equal to the initial velocity plus the

acceleration times time. The next one

says that the position of an object with

respect to a point of origin will be

equal to its initial position plus the

initial velocity times time plus

one-half the acceleration times x

squared.

Lastly, this one says that velocity

squared is equal to the initial velocity

squared plus twice the acceleration

times the displacement. Other

supplemental equations include these two,

which are easily derived from simple

definitions, which state that position is

equal to the average velocity times the

time interval and that the average

velocity is equal to final velocity plus

initial velocity over 2, which is the

definition for any average. Now that we

have these equations and know what all

the variables mean, we are ready to apply

them to real examples of motion. Say you

get in your car to drive to the

supermarket. While at rest, you place your

foot on the gas and apply a constant

acceleration of 2.5 meters per second

squared.

What will your velocity be after 10

seconds and how far will you have

traveled in that time? We can use these

two equations to find the answers, we

just have to plug in what we know. For

the velocity, we know that the initial

velocity was zero because we were at

rest, so we just multiply acceleration by

time and we get 25 meters per second.

That is the velocity of the car after 10

seconds. Now to find how far you will

have traveled, you will use this equation.

Once again, initial velocity is 0 so this

entire term can be ignored.

Then we have one-half times the

acceleration times 10 seconds squared

and we should get a hundred and

twenty-five meters traveled over this

time span. So it really is this simple.

You just choose the equation that is

appropriate for what you are solving for

and plug in what you know. Let's now

consider a car that is already in motion

with a velocity of 27 meters per second.

Let's say you need to stop suddenly so

you press on the brakes,

initiating a rapid deceleration of

-8.4 meters per

second squared. How long will

it take the car to come to a stop and

how far will it travel while your foot

is on the brake? Once again let's use

this equation to solve for time. It must

be this equation because we know

everything in it except for time. For

velocity let's plug in 0 because we are

curious about the time elapsed at the

moment that the car stops moving, and the

velocity when it has stopped moving will

be 0. The initial velocity is the 27

meters per second we mentioned, and we

can plug in the acceleration, solve for

time, and get 3.2 seconds. Now that we

know the time associated with this event

we can use this other equation to find

the braking distance. We plug in the

initial velocity and acceleration we

mentioned before, as well as the 3.2

seconds we just calculated, and solve for

x which will be about 43 meters traveled

from the moment you applied the brakes

to the moment that the car stops moving.

These equations work for any other

object just as they do for cars so let's check comprehension.

Thanks for watching, guys. Subscribe to my channel for

more tutorials, support me on patreon so I can

keep making content, and as always feel

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