16 - Uniform Motion in Physics, Part 1

Summary

This physics lesson introduces the concept of uniform motion in one dimension, explaining it as constant velocity with zero acceleration. The instructor emphasizes the importance of understanding the physics behind equations rather than just memorizing them. The key equation X = X_0 + V_0 * T is presented, illustrating how an object's final position is determined by its initial position, initial velocity, and the time elapsed. The lesson aims to provide a deep understanding of uniform motion, preparing students to solve related physics problems.

Takeaways

• 📚 The lesson focuses on the concept of uniform motion in one dimension, which is a fundamental aspect of physics.
• 🔄 Uniform motion is characterized by an object moving at a constant velocity, meaning it neither speeds up nor slows down.
• 📉 The acceleration in uniform motion is zero because there is no change in velocity.
• 📈 A position-time graph for uniform motion is a straight line, indicating that the object's position changes linearly over time.
• 📊 The slope of the position-time graph represents the velocity of the object, and since the line is straight, the velocity remains constant.
• 🔢 The equation of uniform motion is X = X₀ + V₀T, where X is the final position, X₀ is the initial position, V₀ is the initial velocity, and T is the time elapsed.
• 🧮 Understanding the units in the equation of motion is crucial; velocity (meters per second) times time (seconds) results in distance (meters).
• 📐 The position-time graph's slope is directly related to the object's velocity, with a steeper slope indicating a higher velocity.
• 🔄 The velocity graph for uniform motion is a constant value, reflecting that the velocity does not change over time.
• 📉 The acceleration graph for uniform motion is a flat line at zero, confirming that there is no acceleration occurring.

Q & A

What is the main concept covered in this physics lesson?

The main concept covered in this physics lesson is uniform motion in one dimension.

What is meant by 'uniform motion' in physics?

Uniform motion in physics refers to motion where the velocity is constant, meaning the object is moving at a steady speed without speeding up or slowing down.

How is acceleration related to uniform motion?

In uniform motion, the acceleration is equal to zero because there is no change in velocity, which is the definition of acceleration.

What does a position-time graph look like for an object in uniform motion?

A position-time graph for an object in uniform motion is a straight line with a constant slope, representing the constant velocity of the object.

What does the slope of the position-time graph represent?

The slope of the position-time graph represents the velocity of the object, with the steepness of the line indicating the speed.

What would a velocity graph look like for uniform motion?

A velocity graph for uniform motion would be a horizontal line, indicating that the velocity is constant and does not change over time.

What is the equation of uniform motion?

The equation of uniform motion is X = X₀ + V₀T, where X is the final position, X₀ is the initial position, V₀ is the initial velocity, and T is the time elapsed.

What does the equation X = X₀ + V₀T imply about the relationship between position, velocity, and time?

The equation X = X₀ + V₀T implies that the final position (X) of an object in uniform motion is equal to its initial position (X₀) plus the distance traveled due to its constant velocity (V₀) over a period of time (T).

Why is it important to understand the meaning behind physics equations rather than just memorizing them?

Understanding the meaning behind physics equations is important because it allows for the ability to solve more complex problems and apply the concepts in different contexts, rather than just solving basic problems through memorization.

How does the unit system help in understanding the equation of uniform motion?

The unit system helps in understanding the equation of uniform motion by ensuring that the units on both sides of the equation are consistent, which confirms that the equation is dimensionally correct and physically meaningful.

Outlines

00:00

🚀 Introduction to Uniform Motion in Physics

The paragraph introduces the concept of uniform motion in physics, which is motion in a straight line at a constant speed. The instructor emphasizes the importance of understanding the fundamental concepts of displacement, distance, speed, velocity, acceleration, and instantaneous velocity before delving into the calculations of more complex motions. The goal is to eventually calculate the trajectory of a thrown baseball, including how far, high, and how long it travels. The focus is on one-dimensional motion, where objects can only move in the positive or negative x-direction. Uniform motion is defined as having a constant velocity, which implies zero acceleration, and is graphically represented by a straight line in a position-time graph.

05:01

📈 Graphing Uniform Motion and Its Characteristics

This paragraph delves deeper into the graphical representation of uniform motion, explaining that a straight line in a position-time graph indicates uniform motion due to the constant velocity. The steepness of the line correlates with the velocity, where a steeper line represents a higher velocity and a shallower line indicates a lower velocity. The instructor clarifies that the velocity graph for uniform motion is a horizontal line, signifying that the velocity remains constant. Similarly, the acceleration graph is a flat line at zero, confirming that there is no change in velocity. The paragraph reinforces the idea that uniform motion is characterized by a constant velocity, zero acceleration, and a straight-line position-time graph.

10:03

🧮 The Equation of Uniform Motion and Its Significance

The instructor introduces the equation of uniform motion, X = X₀ + V₀T, where X is the final position, X₀ is the initial position, V₀ is the initial velocity, and T is the time elapsed. The paragraph stresses the importance of understanding the meaning behind the equation rather than just memorizing it. The equation is broken down to explain that the final position is the sum of the initial position and the distance traveled due to the object's constant velocity over time. The units of the equation are also discussed to emphasize that the units on both sides must match, which in this case results in meters. The paragraph concludes by encouraging students to understand the physical meaning behind the equation to solve more complex problems in physics.

15:04

🔍 Deep Dive into the Physics of Uniform Motion

This paragraph continues the exploration of the physics behind uniform motion, focusing on the practical application of the equation X = X₀ + V₀T. The instructor explains that the equation describes the final position of an object based on its initial position and the distance it travels due to its velocity over a given time. The concept of velocity times time equating to distance traveled is emphasized, and the importance of understanding the units and their implications on the equation's outcome is reiterated. The paragraph concludes by encouraging students to move on to solving practical problems using the equation, highlighting that a deep understanding of the equation's meaning is crucial for success in physics.

Keywords

💡Uniform Motion

Uniform motion, as discussed in the video, refers to the type of motion where an object moves at a constant velocity, meaning it does not speed up or slow down. This concept is fundamental to understanding motion in physics, as it simplifies calculations and provides a baseline for more complex scenarios. The video script uses uniform motion to introduce the basic equation of motion, X = X_0 + V_0 · T, where X is the final position, X_0 is the initial position, V_0 is the initial velocity, and T is the time elapsed. This equation is central to the video's theme of teaching how to calculate motion.

💡Velocity

Velocity is defined as the rate of change of an object's position with respect to time. In the context of the video, it is a key component of uniform motion, where the velocity remains constant. The script explains that velocity can be determined from the slope of the position-time graph, which for uniform motion is a straight line, indicating no change in speed. The video uses velocity to illustrate the concept of motion and how it can be quantified.

💡Acceleration

Acceleration is the rate at which an object's velocity changes over time. In uniform motion, as explained in the video, the acceleration is zero because the velocity does not change. The script uses the concept of acceleration to contrast with uniform motion, highlighting that in non-uniform motion, acceleration would be a factor. The video also mentions that the acceleration curve for uniform motion is a flat line at zero, indicating no change in velocity.

💡Position-Time Graph

A position-time graph is a graphical representation of an object's position versus time. The video script uses this graph to illustrate uniform motion, where the graph is a straight line with a constant slope. The slope of this line represents the object's velocity. The video explains that the straight line indicates that the object is moving at a constant speed, which is the essence of uniform motion.

💡Displacement

Displacement is the change in position of an object. The video script mentions displacement in the context of motion, explaining that in uniform motion, the displacement can be calculated using the equation X = X_0 + V_0 · T. Displacement is a vector quantity, which means it has both magnitude and direction, and it is a crucial concept in understanding how far and in which direction an object has moved from its starting point.

💡Instantaneous Velocity

Instantaneous velocity refers to the velocity of an object at a specific moment in time. The video script explains that for uniform motion, the instantaneous velocity is constant and equal to the initial velocity. This is demonstrated in the video by stating that the slope of the position-time graph, which represents velocity, does not change over time.

💡Equation of Motion

The equation of motion, X = X_0 + V_0 · T, is a fundamental equation in physics used to describe the position of an object undergoing uniform motion. The video script emphasizes the importance of understanding this equation, as it is used to calculate the final position of an object given its initial position, initial velocity, and the time elapsed. The video aims to ensure that viewers not only memorize but also comprehend the meaning behind this equation.

💡Units

Units are a critical aspect of physics equations, ensuring that the quantities on both sides of an equation are consistent. The video script discusses how the units of meters per second (velocity) multiplied by seconds (time) result in meters (distance), which is essential for the equation X = X_0 + V_0 · T to be valid. Understanding units helps in verifying the correctness of the calculations and the physical relevance of the results.

💡Initial Position

Initial position, denoted as X_0 in the video, is the starting point of an object's motion. The script explains that in uniform motion, the object's final position can be determined by adding the distance traveled (due to its velocity and the time elapsed) to its initial position. The video uses the initial position as a reference point from which all motion is calculated.

💡Time Elapsed

Time elapsed, represented by T in the video, is the duration of the motion being analyzed. The script emphasizes that in physics, time is typically measured in seconds, which is a standard unit for ensuring consistency in calculations. The time elapsed is a crucial factor in determining the distance traveled during uniform motion, as it is multiplied by the velocity to find the displacement.

Highlights

Introduction to the concept of uniform motion in physics.

Uniform motion defined as motion in one dimension with constant velocity.

Explanation of how uniform motion relates to displacement, distance, speed, velocity, and acceleration.

Uniform motion is characterized by zero acceleration.

Position-time graph for uniform motion is a straight line with a constant slope.

Velocity during uniform motion remains constant, which is represented as a flat line on a velocity-time graph.

Acceleration for uniform motion is zero, as indicated by a horizontal line on an acceleration-time graph.

The equation of uniform motion is derived and explained.

The significance of subscript 'naught' in physics equations is clarified.

Units in physics equations must match to ensure the validity of the results.

The equation X = X₀ + VₙT is broken down to explain its components and their significance.

The concept that velocity times time equals distance traveled is emphasized.

The importance of understanding physics equations beyond just memorization is discussed.

The practical application of the uniform motion equation to real-world scenarios like throwing a baseball.

The lesson's roadmap is outlined, including the description of uniform motion, equation derivation, and problem-solving.

The goal of the lesson is to provide a deep understanding of the uniform motion equation for solving physics problems.

Transcripts

hello welcome back in this lesson in

physics we're going to cover the concept

called uniform motion if you want to

blow it out a little bit bigger it will

be uniform motion in one dimension so

now finally after we've covered the

concepts of displacement and distance

and also speed and velocity and then

finally acceleration and of course

instantaneous velocity instantaneous

acceleration we have all of the

ingredients in place to actually start

calculating how things are going to move

so ultimately what we want to do the end

game is we want to be able to take a

baseball and I want to be able to throw

it at an angle to the ground and then we

want to be able to calculate things like

how far does the baseball go before it

hits the ground again we want to

calculate how high does the baseball go

we want to calculate how long does it in

time how many seconds does it travel and

so on and so that's what we're going but

before we get there we're gonna talk

about motion only in one dimension which

means just this way in that way plus X

and minus X that's the only way that

that these things that we're gonna start

calculating can travel they cannot go up

and down they cannot go to you to the

camera in a way they can only go in the

plus X direction and also in the minus X

direction and so the simplest kind of

motion of any kind is what we call a

uniform motion uniform motion in physics

just means it's a complicated sounding

thing but it just means constant

velocity the velocity is not changing so

uniform motion what does uniform mean it

means an unchanging right so it means

unchanging velocity velocity that

doesn't change so let's talk about that

actually what we're gonna do I'll just

give you the roadmap in this lessons

we're gonna describe uniform motion

we're gonna give it a given the equation

of the uniform motion and then we're

going to squeeze every last bit of

understanding that we can out of that

equation so that you know in your gut

what it actually means and then in the

next lesson we're going to start solving

actual problems so you'll get some

practice with it so what we're gonna do

is start talking about the concept we

just mentioned it's called uniform

motion right and I just said in words

what uniform means there's really it's

really the the same thing that you can

think of it three different ways so the

first way is what I told you is constant

velocity so let's just take a second and

understand what constant velocity means

it means the object is moving but it's

not speeding up and it's not slowing

down

it's just marching along it's some

stately constant values very simple

motion nothing and little real-life

travels at a real constant velocity but

does you have friction and other things

well wind or some something pulling it

like gravity but in this perfect case

we're gonna say things are just moving

along at a constant velocity nothing

ever changes so it stands to reason that

if it's going at constant velocity

another way you could define uniform

motion is that the acceleration is equal

to zero because when you think about it

acceleration means you're changing your

velocity that's what acceleration means

so if it's a constant velocity you're

not accelerating at all you're not

speeding up you're not slowing down so

the acceleration is equal to zero

and then the third way to think about it

which is exactly equivalent to the other

two is you can think of the position the

position time graph which we've been

using all this time we plot the position

versus time graph is a what do you think

it's gonna be it's gonna be a straight

line and this is better illustrated by

example this is exactly what we learned

about when we started talking about this

kind of thing to begin with we plot

position versus time and when everything

is constant meaning the well the

position is not constant the position is

changing but when the velocity is

constant you're just graphing a straight

line in position so let's take just a

second to draw this over here we will

take a case like this we'll draw a

couple of small graphs here this is the

time dimension and this is the position

dimension so when we say in meters let's

call it position versus time this is the

kind of graph we're talking about

remember it's only in one dimension how

far in X am i going as compared to how

time is moving along so if the velocity

is not changing constant velocity that

means the acceleration is zero then the

position time we're saying is a graph of

a straight line which would look

something like this of course you have

some time tick marks down here you know

one second two second three seconds four

seconds or whatever and then you have

some position in meters like once

2 meters 3 meters four meters what is

this basically saying is that time

marches on time never stops its ticking

and ticking and ticking that never stops

but every time another second goes by

notice we travel the same amount of

distance rise of a run

rise of a run every second we go another

chunk of distance in the vertical

direction so what ends up happening is

you're mapping out a line the slope of

this line is never ever ever changing so

the slope of the line might be steeper

say if they have a line going even

steeper I'm going pretty fast here

because I'm getting a lot of distance

down the road for a very short amount of

time if I have a very shallow line like

maybe a line that would go like this

then I'm going very slow my velocity is

slow because as time marches on I'm only

going a little bit farther in X so the

steepness of the line obviously is

related to the velocity we've been

saying that over and over again but in

any case when it's a straight line

position curve that means you're doing

uniform motion now let's go and take a

look that was the velocity graph I'm

sorry that was the position graph let's

look at what the velocity graph would

look like for this curve so this is a

velocity in meters per second so this is

the position for uniform motion is a

straight line that's what we're saying

what do you think the velocity is going

to be what we've said over and over

again that the instantaneous velocity is

going to be the slope and the line

tangent to the position curve but this

position curve is just a line and it

never changes slope so the instantaneous

velocity is the slope of the line

tangent to this thing which just means

it's the slope of this curve at all

points is exactly the same thing so the

velocity here is the same as the

velocity here is the same as velocity

here cuz you're looking at the slope at

those different points and they're all

the same thing so this is the position

the velocity I don't care about units so

I'm not labeling anything but if that's

the position the velocity what do you

think is gonna be it's gonna be a

constant a number that doesn't change

with time notice this could be you know

five meters per second or whatever and

this is time ticking along in seconds

but you notice how the velocity doesn't

change it's nonzero you could be wearing

three meters per second or whatever but

it doesn't change so we say notice the

acceleration zero the position time

graph is a straight line the velocity is

constant these are just different ways

of saying exactly the same thing

uniform motion this is a straight line

because the velocity is constant during

uniform motion now just to round things

out what do you think the acceleration

curve is going to look like in uniform

motion if this is seconds and this is

not velocity this is acceleration what

is the unit of acceleration meters per

second squared right so I can kind of

put this in parentheses meter per second

squared so again look at the pattern the

position curve is this the slope of this

curve at every point defines the

velocity the slope was equivalent every

point so we have a constant velocity and

then we said that the acceleration was

the slope of the velocity curve what is

the slope of this flat line

I mean it's flat the rise over run is

zero because it doesn't rise ever it

doesn't go up it just stays flat so rise

over run is zero so that means the

acceleration curve is going to be zero

down here right so this is zero this is

literally zero this is some constant

positive number and this is the straight

line so the acceleration we're saying is

zero for a uniform motion which is

exactly what we said up here so these

three things it's not like there's three

different things that make it uniform

motion it's all the same thing it's just

there's three different ways to look at

uniform motion is when the position time

graph is a straight line with some slope

which also means the acceleration of

zero which also means it's the the

velocity is constant and we're showing

that through the graphs okay so what is

the equation of uniform motion we're

gonna write that down the equation of

uniform motion all right so this is the

first physics equation you've ever seen

it might look a little scary but I

promise you it is not scary I will

explain every little part of it we say X

is equal to X sub zero you call it X and

knots how you say it plus V not T so I'm

going to circle this because it's the

only thing I'm really trying to get

across in this lesson it's more

important than anything else I'm gonna

go in circle this but you're gonna end

up writing this equation down for every

problem you solve at least in the

beginning and so you're going to

memorize it so don't try to study it

you'll just remember it by using it you

need to get used to the idea of seeing

these little subscripts here like a

like a gold zero this means initial when

you see V naught or X naught it means

initial position or initial velocity

some books will have a little eye down

there to mean to take so you understand

its initial but not is more commonly

used because you're almost always

looking at your you're you're throwing

your baseball or emotion or whatever

you're starting at T equals zero time is

equal to zero and then you're looking at

what happens as time goes on so at x 0 t

0 is the starting position of starting

velocity so the velocity at x 0 we call

V naught the position at time 0 is

called X naught so what this equation is

saying I really want to break it down

I'm not gonna I'm not going to clutter

this one up I'm gonna write the equation

again down below because I'm gonna start

marking all over it but I want to leave

this one alone by itself so X is equal

to X naught plus V naught T if there's

one thing I can impress on you in the

beginning of physics that is going to

serve you all the way through your class

is the following thing you cannot do

well in physics or chemistry or any

other engineering or science or math

class if you just try to memorize

equations and just try to use them like

candy to solve problems without really

understanding what they mean I know that

it's easy in the beginning to solve

problems without really understanding

the equations because a lot of people

will just try to find the numbers from

the problem and they'll stick it in here

and they'll try to find answers but if

you don't really understand the

equations then you will never be able to

solve anything but the most simple

problems so we always start out with

easy problems in physics and then we get

more complicated if you don't know what

this really means

really then you won't ever be able to

construct a complicated solution to

anything but the simple problem so what

I want to try to do throughout this

whole class is give you the equations

but explain to you what they mean so

that you memorize them of course you

have to write them down and use them but

you know what they mean so that they're

not scary little things you're just

trying to like use for no particular

reason

so let's figure out what this equation

is really telling us ok X let me switch

colors here to purple here X notice

we're trying to find the position of

something as we as it's doing some

uniform motion right so X this variable

right here

this one is the final position you're

gonna have to get used to me writing POS

for position because position is too

long of a word I don't like writing it

the units of position or what meters

it's a distance thing right so X is

basically when we finish our motion

where did it end up was it five meters

away well in that case X would be five

did it end up 17 meters away then X

would be 17 what if X ended up being

negative three well if X was negative

three it's not crazy it just means it's

not that way three meters it's this way

X is in the negative direction three

meters so of course X can be positive or

negative and it's just telling you how

far away your thing went whatever you're

talking about car baseball or whatever

all right this one right here a car

already kind of like talked about it a

little bit this is your initial position

what is a unit of initial position

that's also going to be in meters so

almost always when you start a problem

you're going to be starting at position

zero like you'll put a little grid or

it's not really a grid but you'll put a

number line and you're starting the

clock at zero seconds and you're

starting your motion at X is equal to

zero so usually X will be zero and

you'll just stick a zero in there but

sometimes I may give you a problem

especially later when we start doing

other kinds of motion I want to get into

it now you might not start at zero like

maybe I'll give you a problem where the

racecar starts five meters away from the

from the starting point maybe it's not

starting at the at the at the you know

where the lights are with a red yellow

and green lights are maybe the motion is

actually starting from six meters away

from that so that means your initial

position would go in here so literally

this is where you end up and this is

where you start from in meters okay

pretty simple so far now what is T what

do you think T is gonna be that's gonna

be the time elapsed how long my motion

happens and then this guy here let me go

ahead and write this down first I guess

this is gonna be the elapsed time I want

you to always work in seconds a lot of

times problems will be given to you in

like miles per hour or meters per hour

you don't ever shouldn't say never but

you rarely want to work in hours you

just got to get used to dealing with the

fact that in physics you want to deal in

seconds and you want to deal in meters

unless you just

so deal with meters deal with seconds so

that's the time elapsed in seconds

always in seconds maybe have a thousand

in 24 seconds here if you you know a big

number whatever doesn't matter it's

gonna be in seconds now what do you

think this is so it's a V that means

it's a velocity it's got this sub zero

that means it's its initial velocity so

this is the initial velocity right so

what is what are the units of time it's

in seconds what are the units of

velocity it's gonna be meters per second

the reason I'm kind of going through

this is because you can learn a lot

about what equations mean just by

looking at units remember in the very

beginning of the class I told you units

are gonna save your life units can

actually teach you so much about

obviously you have to convert units but

even if you're not converting just

looking at the units of an equation can

tell you everything about what the

equation is so what this equation is

saying in a nutshell is that your final

position where your baseball ends up or

whatever it is is moving it's going to

be equal to wherever it is it starts

from plus something because wherever it

lands is obviously gonna be wherever it

starts from plus something to do with

its motion and whatever we're talking

about motion at least in uniform motion

means it's traveling at a constant

unchanging velocity the velocity is not

changing because it's uniform motion

right and we're multiplying times time

what is that doing so it's really

important for us to take a second to

take a look at what is happening in this

right here so velocity what are the

units of velocity meters per second

right meters per second so if we were

doing a unit conversion with meters per

second and we were multiplying by this

which is seconds then what would happen

remember we talked about unit

conversions you cancel what's on the

bottom and you would end up with meters

so notice what's really happening here

we're saying the final position in

meters is equal to the initial position

in meters plus some other calculation

we'll talk about in a second but when

you do this you end up getting meters

also the units of your equations and

physics should always match if you're

going to get meters for an answer the

only way it can happen is if everything

on the right-hand side add up to meters

that's the only way it can happen if I

have you know if I say that there are 50

jellybeans in a jar jellybeans is my

unit then as I pick out jellybeans I

might say like 10 jellybeans come out

and then five more jellybeans come out

and they add up to 15 I'm saying the

unit of what I'm pulling out of the jar

is jellybeans it has to match with my

answer I cannot have kilograms here plus

meters is gonna give me meters because

that's like adding apples and oranges

doesn't work that way when you get an

answer in meters then you better have

stuff on the right-hand side that add up

and in the units of meters now it's kind

of hidden because this is this is meters

per second times seconds but when you

multiply it out you can see that this

term really is meters and you're adding

it to something here so what is this

actually doing when you take velocity

this is the easiest thing to understand

right when you're going down the road 15

miles an hour right how long how far are

you gonna go in two hours well let's

make it even easier how long are you

gonna go in one hour

if I'm going 15 miles an hour that means

I go an hour that's 15 miles another

hour another 15 miles another hour

another 15 miles so after one hour I've

gone 15 miles after 2 hours you know you

multiply and you're going 30 miles 3

hours it's 45 miles and so on so all

you're doing is you're taking the

velocity times the time and that is what

gives you the total distance that you

travel because of your motion because of

remove Monteux that from driving cars

you know I could go on and on you know 4

meters per second after 2 seconds yeah

four meters 8 minute okay I'm at 8 meter

so I just multiply the two but it from a

unit point of view what's happening is

meters per second times seconds cancel

give you meters so what this is telling

you is this is how far you've moved

strictly due to the motion which is

their velocity which is your velocity

you're given in the problem times how

many seconds has elapsed this is how far

I've moved from A to B where was part AF

a was my initial position so in a

nutshell it's telling you that your

final position of whatever it is is that

that you're throwing like a baseball or

a car or a bow and arrow or something

that travels the final resting place is

going to be equal to wherever it started

from in meters plus how far it traveled

in meters due to its velocity that's the

punchline of this equation so X is equal

to X not

V not T literally is a statement that's

saying hey wherever your land is

wherever you started from plus however

far you traveled due to your velocity

because velocity times time means the

distance traveled that's about all I

want to say in this section if you

understand that which I'm confident

everybody watching this will understand

that then you already understand a lot

more than a lot of physics students

because a lot of times you just read

this equation they're like no I guess

I'll use it I have no idea what it means

but but now you know what it means

you're not just blindly doing stuff for

no reason you have a deep understanding

of the problems so let's go on into the

next lesson let's solve some problems

and you'll see how easy it is to use

this equation to solve simple problems

in motion in physics