Topic 1: Motion and Kinematics
Position
One of the most fundamental concepts in physics is that of position. While position might seem
like a simple enough concept, like pointing to something, to describe an object's position
scientifically requires th
ree things.
Imagine you were trying to describe the position of Sioux Falls to someone who is unfamiliar
with the geography of the Midwest. The first thing you might try to do is describe the distance, or
displacement, to Sioux Falls. While this might s
eem easy enough, you have to take into
consideration what kind of units you're going to use. Distance can be described in a variety of
units, including miles, kilometers, feet, meters, and so on.
Such units are broken up into two categories: standard a
nd metric. Standard units, such as
inches, feet, yards, and miles are the ones we use in the United States, while the rest of the world
uses the metric system, with units like meters, centimeters, kilometers, and millimeters. Now, you
might be wondering wh
y the rest of the world would use a different system than the US, and it
has to do with ease of conversion.
Most people know that there are 12 inches in a foot and 3 feet to a yard. And while some people
remember that there are 5,280 feet in a mile, not
many could tell you off the top of their heads
how many
yards
are in a mile. The problem is that there aren't any logical conversions between
the standard units. The metric system, on the other hand, is all based on units of 10. There are 10
millimeters i
n a centimeter, there are 100 (10x10) centimeters in a meter, and there are 1000
(10x10x10) meters in a kilometer.
But just telling someone how far it is to Sioux Falls isn't enough. In order for that distance to
make sense, we also have to know how far
it is from
where
. We need what's called a reference
point. A reference point is just some object, place, or location that is already known to everyone
involved. It could be a table, a door, a street corner, a city, or even you. For example, I could say
th
at your computer monitor is two feet in front of
you
. Or in the case of Sioux Falls, we could say
that it is 75 miles
from Sioux City
.
So we have distance and we have a reference point, but we still need one more thing for our
position to make sense. If
you think about saying that Sioux Falls is 75 miles from Sioux City, you
might realize we're missing something important. Just saying "75 miles from Sioux City" doesn't
refer to just Sioux Falls, it refers to
everything
75 miles from Sioux City. "75 miles
from Sioux City"
actually describes a huge circle all the way around Sioux City, with Sioux Falls lying somewhere
on that circle. To be entirely accurate in the position of Sioux Falls, we also need the
direction
of
Sioux Falls relative to Sioux City.
Once we have a direction, we're set. To describe the position of Sioux Falls, we could say it's 75
miles (distance) north (direction) of Sioux City (reference point).
And while on the topic of distance, there's one more thing to discuss, and that's the
difference
between distance and displacement. While they are often used interchangeably, they are not the
same thing. Specifically, distance is defined as how far you've gone, while displacement is
defined as how far you are from where you started. These d
efinitions might sound similar, but a
simple example can point out the difference. Let's say I drove to Sioux Falls. When I arrive, I find
that the two values are the same, since I've driven 75 miles (distance) and I'm 75 miles from
where I started (displa
cement). The difference arises when I drive back. When I get home, my
distance is now 150 miles, but my displacement has dropped to 0, because I'm right back where I
started.
Velocity
Now that we've talked about distance, the next step would be to talk
about how long it takes us
to move that distance, and, more importantly, how fast we're going while we're moving. The rate
at which we're moving is called speed, or velocity, and the faster we go, the less time it takes to
move a particular distance. For
this reason, speed is often described as the distance traveled
divided by the amount of time it takes us. And, as such, the units for speed are described by the
units of distance "per" the units of time: miles per hour, meters per second, feet per minute,
and
so on.
There are actually two types of speed. The first is the one we're probably more familiar with,
called instantaneous speed, or how fast we're going
right now
. When you check your
speedometer, what you're looking at is instantaneous speed.
Now, sometimes you might also want to figure out what's called your average speed. Average
speed is not, as you might imagine, an average of speeds. Instead, it is defined as the total
distance traveled divided by the total time.
For example, let's say
we're driving to Sioux Falls from Sioux City, and let's say the distance is a
total of 90 miles. For the first part of the trip, up until McCook Lake, the speed limit is 65. (And
let's pretend we're actually going the speed limit.) Then there's a long sect
ion where we're driving
at 75 miles per hour. But then, as usual, somewhere in the middle we have to slow down to 55,
and then 45, for construction. But once we're through that, it's back up to 75 for the rest of the
trip.
Now, let's say it ends up tak
ing us a total of 75 minutes to make the whole trip. If we just
average those five speeds together, we end up with an average of 63 mph, but that doesn't make
any sense, since we traveled at 75 for most of the trip. If, instead, we take the total distance
traveled, 90 miles, and divide by the total time, 75 minutes or 1.25 hours, we obtain an actual
average speed of 72 mph, which makes more sense.
You may have noticed that the title for this section is actually speed
and
velocity. That's
because, much li
ke distance and displacement, speed and velocity are two terms that are often
used interchangeably, but actually have a technical difference between them. Specifically, speed
is how fast you're going, while velocity is how fast you're going
and
in what dir
ection. In other
words, velocity is both speed
and
direction.
Acceleration
If speed is a change in distance with respect to time, then what would we call a change in
speed
with respect to time? Well, when you're reading about the latest sports car and
the ad says it can
go from 0 to 60 in 5 seconds, what is it telling you? It's telling you how fast the car can accelerate,
so a change in speed with respect to time is called an acceleration.
By the way, usually when you think of a car "accelerating", y
ou might only think of it speeding
up. In science, however, acceleration is defined as
any
change in velocity with respect to time, so
even slowing down, or decelerating, is technically considered acceleration.
Now, what's interesting about acceleration
is that it's something you can actually
feel
. Okay,
imagine you were kidnapped by CIA operatives, stuffed in a van, and knocked out. When you
wake up, you find yourself bound and blindfolded, and the van has
really
good shocks. In that
state, can you thin
k of any way you could tell if the van was moving? You're blindfolded, so you
can't see, and the really good shocks prevent you from feeling the bumps and jostles of the road,
so how could you tell if the vehicle was actually moving or not? The simple answ
er is, as long as
the vehicle maintains a constant velocity, you can't. If the van were to speed up or slow down, if it
changed its velocity though, you could "feel" that, you could feel the acceleration, and you would
know that you were moving.
Imagine
you're riding with a friend and he steps on the gas and peels out. You'd feel yourself
thrown back in the seat, right? And if he suddenly slammed on the brakes, you'd feel yourself
thrown into the windshield. Both of those are examples of acceleration. Th
e thing is, you could
also feel like you're being thrown into the passenger door window if your "friend" turned a corner
too fast, right? That's because acceleration isn't just slowing down or speeding up, acceleration
can also be a change in
direction
. Ac
celeration isn't just a change in speed, it's a change in
velocity
, which means if your speed
or
direction changes, it's considered an acceleration. When
the car turns suddenly, it's technically accelerating, which is why you slam into the window just as
y
ou would slam into the windshield or be pulled back in your seat when the car's speed changes.
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