### Motion in a Straight Line: Crash Course Physics #1

Hi, I’m Dr. Shini Somara and I hear you

want to learn physics. I have to say: good choice. Physics is the science of how the world — really

the whole universe — works. And I don’t know if you’ve noticed, but

in the world I live in, things tend to move around a lot. So that’s what we’re going to study first:

the science of motion. And it turns out to be incredibly useful — for

figuring out things like where you are, or where you’ve been, or how you’re moving

through the world. Why is that worth knowing? Well, for one thing: The police use physics

to decide how exactly how fast you’re moving through the world, and if that motion happens

to break the law. So if you’re gonna understand how and why

you got that ticket they gave you — and maybe even know enough to dispute it — you have

to know the science of motion, too. And in order to do that, you’ll need to

understand a few essential conditions that describe your physical place in the universe. Conditions like time, position, velocity,

and acceleration. So to talk about all of these things at the same time, you’ll need a set of equations that links all of them together. These are called the kinematic equations. So, for the next few minutes, let’s talk

about how you can figure out your place in the world — literally — which just might

help you beat that speeding ticket. [Theme Music] Let’s say you’re driving on a straight stretch

of highway. Say, someplace nice and flat, on the wide open spaces of the Northern

Plains of the United States. Say…North Dakota. You come across a red light, and even

though there are no cars in sight, you stop. Because you’re a good driver who obeys traffic laws. Then, the light turns green, so you hit the

gas. Annnnd exactly seven seconds later, you hear the sirens and see the flashing lights

of a police car. You’re promptly served with a ticket for

speeding in a 100 kilometer an hour zone. But wait. Were you really going that fast?

Did you actually break the law? You can’t really tell, because the

speedometer in your car is broken. So you need to find another way to figure

out how fast you were going, and decide if you want to take this up this issue with Johnny

Law in court. That’s where physics comes in — the physics

of moving in a straight line. Let’s start by talking about how your car

was moving. Driving along a straight highway is an example

of one-dimensional motion because the car can only move back and forth along that line. That’s different from something that’s

free to move in all three dimensions, like a boomerang flying through the air. And instead of describing that motion just

in terms of speed, or direction, like a police officer or other non-physicist might do, we

physicists describe it with math. Maths that measures the four main

conditions of the car’s movement — its time, position, velocity, and acceleration. Time simply tells you how long you were driving

for. Position is also important: It lets you know where you are or where you were. It can

even be negative. For one-dimensional motion, there are only

two directions you can move in — in this case, forward or backward, east or west. So, if the change in position — known as

displacement — is positive, you’ll know you’ve moved in one of those directions.

If it’s negative, you’re traveling the other way. But which direction is positive, and which

is negative? That’s totally arbitrary. You could decide that east should be positive

and west negative, or the other way around — but the answers you get will mean the same

thing. You just have to make sure to keep track of

which direction is positive, and keep that in mind when you’re talking about velocity

and acceleration, too. Velocity is the way your position changes

over time, and it’s also a pretty big deal. It’s kind of like speed, but just like with

displacement, it also tells you which direction you’re moving in, based on whether it’s

positive or negative. Now, what about when your velocity changes? That’s the fourth quality of movement you’ll

want to pay attention to: acceleration. If you’ve ever been in a car when someone

slammed on the gas, that feeling of being pressed back against your seat is acceleration

— your velocity’s changing. So, how do we plot out all of these different

conditions that describe the movement of you and your vehicle through the plains of North

Dakota? A non-physicist might visualize this movement

on something like a map, but for us, graphs are the most useful way to show how all this

change in position is happening. Graphs are generally presented as position

versus time — with position on the vertical axis, and time on the horizontal axis. We’ll label your position as x and time

as t. Now, let’s imagine three different scenarios for how you drove through this small town, and graph each one. First, let’s say that, after you went through

the red light, you just stayed in one spot — say, at 4 meters from the light — for

three seconds. From that moment, the graph of your position

would just be a flat line at x=4 m, like this. Now, what if you didn’t stop, but instead

were coasting at one meter per second? Then the line would be diagonal, to show how

your position was changing — like this. And the third time, let’s say you were standing still at first at the 4 meter mark, but then you hit the gas, and you moved in such a way that,

after 1 second, you went 1 meter in the positive direction and after 2 seconds you went 4 meters

and after 3 seconds you’ve gone 9 meters. In that case, you end up with a graph that’s

all curvy, like this. But there’s more going on in these

scenarios than just your position and time. You also have to be able to graph your

velocity and acceleration. So, to graph your velocity, you’d put your velocity on the vertical axis and time on the horizontal axis. And you’ll note that, since velocity is

measured as the change in position over time, it’s measured in meters per second. The graph for acceleration is quite similar — acceleration, a, goes on the vertical, and time goes on the horizontal. And since acceleration is measured as the

change in meters per second, its units are meters per second per second — otherwise

known as meters per second, squared. So: time, position, velocity, and

acceleration all relate to each other. Velocity is the change in position over time, and acceleration is the change in velocity over time. And often, your velocity will be different

from moment to moment — like the third time you drove down the highway, when you hit the

gas. But let’s say you wanted to know your average velocity for a certain period — say, for those first three seconds. All you have to do is take the change in position

and divide it by the change in time. Figuring out how much something is changing just means that you have to subtract its starting value from its final value. And since, as physicists, we’ll end up doing

that a lot, we abbreviate that difference using the lowercase Greek letter delta. So we can use that to write the equation for average velocity: It’s just delta x over delta t. The change in position over the change

in time. Now what about the third scenario? When you

had your foot on the gas and kept accelerating? You started out at the 4 meter mark, and ended

up at the 13 meter mark. So your change in position, or delta-x, would be 13 minus 4,

or 9 meters. And you started at 0 seconds and ended at

3 seconds, meaning that your delta-t was 3 seconds. Over 3 seconds, you moved 9 meters. That’s

3 meters per second! The equation we use to describe average acceleration

is a lot like the one for average velocity, because it’s just the change in velocity

divided by the change in time. So, in that case, your equation would be delta

v over delta t. And! Here’s something that is incredibly

handy. Since we’re talking about constant acceleration

— that is, acceleration that takes place at a constant rate — we can rearrange this

equation to get v=v_0 + at. That’s average velocity equaling to velocity at time 0 plus the product of acceleration times time. This, my fellow physicists, is an equation

we’ll be using a lot. We call it the definition of acceleration

— because that’s exactly what it is. It’s saying that constant acceleration is equal to the change in velocity divided by the change in time — we just used algebra to move the

variables around. Now, it’s worth noting that there are lots

of different kinds of acceleration, ones that don’t involve speeding tickets —

like when something is falling. The force of gravity pulling it down is making

it accelerate at 9.81 meters per second squared, which physicists often abbreviate as a lowercase

g. So we’ll just call that constant small g

… there’s a capital G that’s going to come up later. So, the definition of acceleration is the

first of the two main kinematic equations that we’ll be using. But it only links velocity,

acceleration, and time. What about position? There’s an equation for that too — the

second kinematic equation, which we’ll call the displacement curve, because it takes your

acceleration, your starting velocity, and how long you were moving for, and uses that

information to figure out what your displacement was. And the displacement curve equation looks

like this. It makes sense, if you think about it — if

your acceleration is the change in your velocity, and your velocity is the change in your position, then there should be some way to link all of them together. Now, there are lots of other kinematic equations,

too, like these. But, you only really need to know the first

two — the definition of acceleration and the displacement curve. The others are just

different ways of rearranging these main two. And because these two equations have so many terms in common, you can use them together really easily. For example, if you know your acceleration,

and your starting and final velocities, you could use the definition of acceleration to

figure out how much time you were traveling for. Then you could plug that value for time into the displacement curve equation and use it to find your displacement. Now that we know what the kinematic equations

are, we can finally use the power of physics to find out whether you were speeding when

the cops pulled you over. As with most physics problems, the first thing

we need to do is write down everything we know. In this case, we know your initial velocity,

v-nought, was 0, and your time, t, was 7 seconds. The first thing we need to find is your acceleration,

which we can get using the displacement curve. Plugging in everything we know, we find that

your acceleration, a, was 5 meters per second squared. Then, we can plug all of that into the definition of

acceleration, to find your final velocity, like this: We learn that you were going 35 meters per

second when the cops pulled you over. That’s 126 kilometers an hour…

So you definitely deserve that ticket. Sorry. But, in this very first episode of Crash Course Physics, you learned all about position, velocity, and acceleration. We also talked about the two main

kinematic equations: the definition of acceleration,

and the displacement curve. Crash Course Physics is produced in association

with PBS Digital Studios. You can head over to their channel to check out amazing shows

like Deep Look, The Good Stuff, and PBS Space Time. This episode of Crash Course was filmed in

the Doctor Cheryl C. Kinney Crash Course Studio with the help of these amazing people and

our Graphics Team is Thought Cafe.

9:39 How do you find that out?

It's much more simple to turn the minutes into seconds such as

3 minutes = 180s and then dividing it by the distance which is the amounts of meters traveled, in this case we'll say 500

500/180 = 2.77 m per second.

9:21 finally solved for something

this goes so fast and way over my head ohmygod

👍

Slight Correction: The number you find at the end of the video is not average velocity of the whole trip, it's the final velocity at the time of being pulled over.

how do you get a = 5 m/s?

Nice Focus SVT, one way to distract a car guy

U were the one who did chemistry atomic structure. Like if u are a human.

Am I the only one who thinks this women is hot?

Actually I am not having a formula 1 to do 126kmph I 7 seconds

Helped me so much! Love these vids!🙏

6:22

that… that's an uppercase delta….

A little confusing around 7:30?

average velocity = initial velocity + acceleration * time /2

final velocity = initial velocity + acceleration * time

and that delta is uppercase

I can see myself mathematically explaining to a police officer why i wasn’t speeding

High school blew chunks but learning year 11 and 12 physics were some of my fondest memories. Will look forward going through this series as I have other Crash Course videos. Lol North Dakota sign. 'Not South Dakota.'

Cop – Here's your ticket for over-speeding….

Driver – wait for a minute…..let me use the kinematic equations to see if this is true.

uppercase delta?

They said nothing about 122 meter distance when introducing the problem and started talking about 9 meter distance example. It was very confusing for a beginner as myself :/

To know what is your average acceleration you just need to multiply the distance by 2 and divide it by the time squared. For example you went 100 meters in 5 sec. It means that your acceleration is 200/25= 8m/s2

Let's say I went 100 meters in 5 sec and now I'm going about an hour. I'm going this long distance and I'm not sure if there's an acceleration? My speedometer is broken. What if I'm going evenly? I'm not sure about it. What to do in this case?

9:39 How is a=5 m/s²? When I convert the formula to a I get 244/7 m/s²

What is armor penetrating phisics?

how did she get the acceleration at 9:40?

Why is this messing with my head ?

7:28 | Average velocity = initial velocity + acceleration * time

shouldn't it be | final velocity = initial velocity + acceleration * time ?

shouldn't average velocity be | Average velocity = initial velocity + (acceleration * time ) / 2

I saw your physics videos for my exam and I got 100% in physics. Thanks ❤

She sounds identical to Hermione. (Emma Watson)

i cant keep up….i cant even take notes

Is this on a GCSE or A Level Physics Course?

Damn, as not native english Speaker, slow down, like a hell of a lot down, damn I had to pause and rewind like 13 times

First episode, and I'm already lost.

Slow down your speed of talking. If you do this, you will be more effective.

you would still get a ticket

excellent

You're talking so fast that I can't compose everything

Her: "I hear you want to learn physics."

Me, being a pessimist: "No I want to pass my test tomorrow and nothing my teacher taught me makes sense."

Video goes way too fast for anyone that actually wants to learn physics. If you already have a good understanding then I'm sure it's fine. I'd rather have a 25 minute video that actually explains the science instead of a rushed 10 minute video.

Thank you!!

7:27 pretty sure that's like a stomach growl in the background

oh and The vid helped a lot btw thankssss!!

My brain hurts

thank you Dr. Shini Somara!

you are a better teacher than my professors. i feel i get all the goodsides upsides no downsides. glad this is free. better than university classes.

5:37 DAMN THAT ALWAYS CONFUSED ME NEVER KNEW Y IT WAS SECONDS SQUARED

Doesnt the v in v = v0 + at mean velocity at time t not average velocity?

~~Gets pulled over by the cops~~~~pulls out notepad,calculator and Jimmy Neutron science~~~~argues with the cops with said science for about 15 minutes only to realize I was wrong~~Next time I’ll just take the ticket thx 😓

Quick tip guys, slow down the video. It sounds a little distorted, but after a minute you don't even notice it. It's easier to keep up and relate to what she is saying. A lot of people speed up when teaching cause there so much information and so little time to say it. The beauty of this is you can slow down their time to your liking

i don't get it

I don't get why you flash equations up there for half a second and show her face almost constantly. I think I'd get more out of it with a lot less face time and maybe somebody doing actual calculations on screen.

her: introduces math equation in science

me: mouth dropping in horror

You clearly got A's in exams lol

This video has great information but I feel like pouring information, and no time to digest = overwhelming over velocity

what what wha wha wha all i hear is mate mate good day

Me an American when she said kilometers: wtf?

This only confused me more.

Isn't the "average velocity" in the definition of acceleration equation actually final velocity, not the average? Delta v is Vfinal minus Vinitial, not Vaverage minus Vinitial. Can we get… an updated video? That's bound to confuse my students.

The entire section about average velocity seemed out of place. The measurement is fine for some situations, but in a study of kinematics it becomes problematic if it's just thrown out there.

1:44 big foot under the trees…👀

is anyone else rly confused by how she got the answer to the equation at 9:37 ?? I'm so lost lmao

This woman is heavenly

I cant follow this thought exercise because of the 100km per hour limit in North Dakota USA

امتحان فزكس باجر 😒😒💔 !

Fk all i heard was like"mterss mters blah blah x t"

in my school we learned that velocity is the direction and speed

Bruh y is she talkin like eminem

This is great at 1.5 speed

My brain: reduce the playback speed… Me: ok , 0.75. Reads comment, woman talking ..my brain, she's still fast. Me: 0.50 🙄 now even the music is slow motion. This is ridiculous. I'm dropping Physics class …we can/t keep up with the jibber jabber..

Ok, ok I got this!

You lost me at “so you want to learn physics?”

Her voice is (almost) as fast as hanks

Congrats!

Im 11 and i kinda understand a little bit

How do I learn this when I’m in 7th grade

Put on subtitles and slow down the speed of the video to 0.5. Thank me later. <3

very helpful

This presenter goes so fast that even though I knew this stuff she makes my brain melt. Slow down. PLEASE.

Easier to understand at .75 normal speed.

The Displacement Curve gets about 3 seconds of explanation. Not very helpful.

WTF is displacement anyway

Now I now :0

I’m here to cram for my exam in the next 24 hours

caree

When is physics going to die????

Umm…..

o.O

I am confused

who has there IGCSE's tomorrow

I would die for her accent oh my gahsh-

Crash course DEBATING!!! please oh please!

Breathe, please. If you run a lesson like in school… what's the point of this course?

Unluckily I think this is the worst crash course series; sorry but this "teacher" is just running as the majority of bad teachers of Maths and Physics in school. I repeat, if so, what's the point of this course? A pity because it's one of my favorite subjects.

Smart idea

I really miss this series, and it's host.

How did you find out a with the displacement curve method, I don't get it 🤔

I am more lost than I was before….

Change your playback speed to 0.75X and thank me later

You would think that such an attractive, seemingly motivated girl would strive to ameliorate her impoverished circumstances by at least trying to get some form of missionary instructed schooling, or rudimentary education?

… sad, such a waste :•(

I get to learn in bed? Up for it.

1:10 i so totally beat up speeding tickets with Doppler radars using physics equations!

Oh and i love this young lady and her energy 🙂

Yes police officer my delta v over t was less then your observation. In the trump usa you get shot for that. You must be a terrorist .

trash learning

Did anyone watch that all the way through?

Use playback speed at 0.75.

thank me later 😉

1:43 big foot

Her accleration in wpm is 1000