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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