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Hi, I’m Dr. Shini Somara and I hear you
want to learn physics.
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I have to say: good choice.
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Physics is the science of how the world -- really
the whole universe -- works.
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And I don’t know if you’ve noticed, but
in the world I live in, things tend to move around a lot.
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So that’s what we’re going to study first:
the science of motion.
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And it turns out to be incredibly useful -- for
figuring out things like where you are, or
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where you’ve been, or how you’re moving
through the world.
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Why is that worth knowing?
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Well, for one thing: The police use physics
to decide how exactly how fast you’re moving
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through the world, and if that motion happens
to break the law.
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So if you’re gonna understand how and why
you got that ticket they gave you -- and maybe
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even know enough to dispute it -- you have
to know the science of motion, too.
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And in order to do that, you’ll need to
understand a few essential conditions that
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describe your physical place in the universe.
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Conditions like time, position, velocity,
and acceleration.
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So to talk about all of these things at the same time,
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you’ll need a set of equations that links all of them together.
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These are called the kinematic equations.
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So, for the next few minutes, let’s talk
about how you can figure out your place in
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the world -- literally -- which just might
help you beat that speeding ticket.
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[Theme Music]
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Let’s say you’re driving on a straight stretch
of highway. Say, someplace nice and flat,
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on the wide open spaces of the Northern
Plains of the United States. Say…North Dakota.
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You come across a red light, and even
though there are no cars in sight, you stop.
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Because you’re a good driver who obeys traffic laws.
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Then, the light turns green, so you hit the
gas. Annnnd exactly seven seconds later,
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you hear the sirens and see the flashing lights
of a police car.
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You’re promptly served with a ticket for
speeding in a 100 kilometer an hour zone.
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But wait. Were you really going that fast?
Did you actually break the law?
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You can’t really tell, because the
speedometer in your car is broken.
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So you need to find another way to figure
out how fast you were going, and decide if
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you want to take this up this issue with Johnny
Law in court.
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That’s where physics comes in -- the physics
of moving in a straight line.
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Let’s start by talking about how your car
was moving.
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Driving along a straight highway is an example
of one-dimensional motion because the car
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can only move back and forth along that line.
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That’s different from something that’s
free to move in all three dimensions,
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like a boomerang flying through the air.
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And instead of describing that motion just
in terms of speed, or direction, like a police
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officer or other non-physicist might do, we
physicists describe it with math.
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Maths that measures the four main
conditions of the car’s movement --
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its time, position, velocity, and acceleration.
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Time simply tells you how long you were driving
for. Position is also important: It lets you
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know where you are or where you were. It can
even be negative.
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For one-dimensional motion, there are only
two directions you can move in --
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in this case, forward or backward, east or west.
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So, if the change in position -- known as
displacement -- is positive, you’ll know
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you’ve moved in one of those directions.
If it’s negative, you’re traveling the other way.
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But which direction is positive, and which
is negative? That’s totally arbitrary.
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You could decide that east should be positive
and west negative, or the other way around
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-- but the answers you get will mean the same
thing.
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You just have to make sure to keep track of
which direction is positive, and keep that
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in mind when you’re talking about velocity
and acceleration, too.
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Velocity is the way your position changes
over time, and it’s also a pretty big deal.
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It’s kind of like speed, but just like with
displacement, it also tells you which direction
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you’re moving in, based on whether it’s
positive or negative.
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Now, what about when your velocity changes?
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That’s the fourth quality of movement you’ll
want to pay attention to: acceleration.
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If you’ve ever been in a car when someone
slammed on the gas, that feeling of being
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pressed back against your seat is acceleration
-- your velocity’s changing.
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So, how do we plot out all of these different
conditions that describe the movement of you
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and your vehicle through the plains of North
Dakota?
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A non-physicist might visualize this movement
on something like a map, but for us, graphs
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are the most useful way to show how all this
change in position is happening.
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Graphs are generally presented as position
versus time -- with position on the vertical
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axis, and time on the horizontal axis.
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We’ll label your position as x and time
as t.
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Now, let’s imagine three different scenarios for how you drove through this small town, and graph each one.
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First, let’s say that, after you went through
the red light, you just stayed in one spot
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-- say, at 4 meters from the light -- for
three seconds.
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From that moment, the graph of your position
would just be a flat line at x = 4 m, like this.
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Now, what if you didn’t stop, but instead
were coasting at one meter per second?
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Then the line would be diagonal, to show how
your position was changing -- like this.
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And the third time, let’s say you were standing still at first at the 4 meter mark, but then you hit the gas,
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and you moved in such a way that,
after 1 second, you went 1 meter in the positive
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direction and after 2 seconds you went 4 meters
and after 3 seconds you’ve gone 9 meters.
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In that case, you end up with a graph that’s
all curvy, like this.
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But there’s more going on in these
scenarios than just your position and time.
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You also have to be able to graph your
velocity and acceleration.
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So, to graph your velocity, you’d put your velocity on the vertical axis and time on the horizontal axis.
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And you’ll note that, since velocity is
measured as the change in position over time,
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it’s measured in meters per second.
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The graph for acceleration is quite similar -- acceleration, a, goes on the vertical, and time goes on the horizontal.
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And since acceleration is measured as the
change in meters per second, its units are
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meters per second per second -- otherwise
known as meters per second, squared.
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So: time, position, velocity, and
acceleration all relate to each other.
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Velocity is the change in position over time, and acceleration is the change in velocity over time.
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And often, your velocity will be different
from moment to moment -- like the third time
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you drove down the highway, when you hit the
gas.
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But let’s say you wanted to know your average velocity for a certain period -- say, for those first three seconds.
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All you have to do is take the change in position
and divide it by the change in time.
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Figuring out how much something is changing just means that you have to subtract its starting value from its final value.
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And since, as physicists, we’ll end up doing
that a lot, we abbreviate that difference
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using the lowercase Greek letter delta.
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So we can use that to write the equation for average velocity: It’s just delta x over delta t.
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The change in position over the change
in time.
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Now what about the third scenario? When you
had your foot on the gas and kept accelerating?
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You started out at the 4 meter mark, and ended
up at the 13 meter mark. So your change in
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position, or delta-x, would be 13 minus 4,
or 9 meters.
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And you started at 0 seconds and ended at
3 seconds, meaning that your delta-t was 3 seconds.
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Over 3 seconds, you moved 9 meters. That’s
3 meters per second!
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The equation we use to describe average acceleration
is a lot like the one for average velocity,
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because it’s just the change in velocity
divided by the change in time.
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So, in that case, your equation would be delta
v over delta t.
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And! Here’s something that is incredibly
handy.
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Since we’re talking about constant acceleration
— that is, acceleration that takes place
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at a constant rate — we can rearrange this
equation to get v = v_0 + at.
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That's average velocity equaling to velocity at time 0 plus the product of acceleration times time.
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This, my fellow physicists, is an equation
we’ll be using a lot.
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We call it the definition of acceleration
-- because that’s exactly what it is.
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It’s saying that constant acceleration is equal to the change in velocity divided by the change in time --
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we just used algebra to move the
variables around.
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Now, it’s worth noting that there are lots
of different kinds of acceleration,
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ones that don’t involve speeding tickets --
like when something is falling.
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The force of gravity pulling it down is making
it accelerate at 9.81 meters per second squared,
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which physicists often abbreviate as a lowercase
g.
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So we’ll just call that constant small g
… there’s a capital G that’s going to come up later.
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So, the definition of acceleration is the
first of the two main kinematic equations
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that we’ll be using. But it only links velocity,
acceleration, and time. What about position?
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There’s an equation for that too -- the
second kinematic equation, which we’ll call
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the displacement curve, because it takes your
acceleration, your starting velocity, and
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how long you were moving for, and uses that
information to figure out what your displacement was.
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And the displacement curve equation looks
like this.
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It makes sense, if you think about it -- if
your acceleration is the change in your velocity,
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and your velocity is the change in your position, then there should be some way to link all of them together.
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Now, there are lots of other kinematic equations,
too, like these.
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But, you only really need to know the first
two -- the definition of acceleration and
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the displacement curve. The others are just
different ways of rearranging these main two.
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And because these two equations have so many terms in common, you can use them together really easily.
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For example, if you know your acceleration,
and your starting and final velocities,
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you could use the definition of acceleration to
figure out how much time you were traveling for.
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Then you could plug that value for time into the displacement curve equation and use it to find your displacement.
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Now that we know what the kinematic equations
are, we can finally use the power of physics
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to find out whether you were speeding when
the cops pulled you over.
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As with most physics problems, the first thing
we need to do is write down everything we know.
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In this case, we know your initial velocity,
v-nought, was 0, and your time, t, was 7 seconds.
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The first thing we need to find is your acceleration,
which we can get using the displacement curve.
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Plugging in everything we know, we find that
your acceleration, a, was 5 meters per second squared.
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Then, we can plug all of that into the definition of
acceleration, to find your final velocity, like this:
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We learn that you were going 35 meters per
second when the cops pulled you over.
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That’s 126 kilometers an hour…
So you definitely deserve that ticket. Sorry.
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But, in this very first episode of Crash Course Physics, you learned all about position, velocity, and acceleration.
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We also talked about the two main
kinematic equations:
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the definition of acceleration,
and the displacement curve.
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Crash Course Physics is produced in association
with PBS Digital Studios. You can head over
00:10:14
to their channel to check out amazing shows
like Deep Look, The Good Stuff, and PBS Space Time.
00:10:20
This episode of Crash Course was filmed in
the Doctor Cheryl C. Kinney Crash Course Studio
00:10:25
with the help of these amazing people and
our Graphics Team is Thought Cafe.
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