 ### 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.