Where is the ball?
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Where is the table?
Where is the floor?
Where is the school?
Where is the city?
Where is the state?
Where is the country?
Where is the world?
Where is the solar system?
Where is the galaxy?
Where is the universe?
We can’t say where anything is
without saying where something
else is!
• But what exactly is “where”?
• Where describes the position of some object
as compared to the position of some other
object.
• But what does position mean?
• Position – A point in space compared to
some other point in space.
Position. The details.
• The problem is that we don’t know what
some of the terms in this definition really
mean.
• For example: What, exactly, is a point, and
what is space?
• Point – This is a mathematical point that
has no dimensions. A point is a spatial
(having to do with space) marker.
What is space?
• This space is a not just outer space, or inner
space, or empty space. Space is all space.
• Make a three dimensional coordinate
system and stretch the axis out to infinity.
You have just identified all of space.
• Note that space can be filled (like the inside
of this table top), or empty.
y
z
x
What is compared?
• Compare – to show the similarities and
differences between two or more different
things.
• In physics we have another word for
compared. This word is similar to the word
we have for Fathers, and mothers, and
brothers, and sisters.
• Relative – Compared to.
This gives us a revised definition
for position.
•Position – A point
in space relative to
some other point in
space.
What is time?
• Time is not the moment, second,
minute, hour, day, year etc.
• Those are terms used to describe how
we measure time.
• They don’t tell what time is.
• What are some other ways in which we
tell time?
Write down the things you’ve
done today, in order, up till now.
• What does that list have in common with all the ways
we measure time?
• What is another word for the “things” you did today?
• If the best band in the world were coming to town today,
that would be a major __?__.
• Note: Not all events are major.
• Event –something that happened.
• The second hand goes from the 12 to the first click after
the twelve. One second, event # 1. Etc.
• So, what we did was to order our events of our day. Just
like the clock does.
So what is time?
•Time – The ordering of
events.
Motion!
• Describe what happens when some thing
moves.
It goes (lets say) from position A to position B
A
B
What about time?
• Can an object move from point a to point b
without time passing?
• NO!
• Nothing can occupy two different positions
at the same time!
• This means that if the position changes, the
time must also change.
Motion defined!
•Motion – the change in
position with respect to
the change in time!
Is the ball on the table moving?
• By the definition of motion, you can see that
the ball is not moving because its on the same
spot on the table.
• But the table is on the earth, and the earth is
moving around the sun, and the sun is moving
around the galaxy, and the galaxy is moving
through the universe! This ball is really
moving!
• But no, its still on the same spot on the table!
• How do we resolve this dilemma!
The answer is not a simple yes or
no!
• Compared to the table, the ball is not moving.
Compared to the sun the ball is moving.
• What was the word for compared to?
• To answer the question, we must speak of
relative motion!
• The correct answer is:
• Relative to the table, the ball is NOT moving.
• Relative to the sun, or any non-earth
astronomical entity, (or really any thing that is
moving relative to the ball) the ball IS moving!
You can’t tell!
• Put your hands in front of your eyes so
all you can see is the whiteboard and me.
• As the white board moves behind me
you can’t tell if the white board is
moving or if I am moving. Except, of
course, you know the white board can’t
be moving so it must be me that is
moving, so your brain convinces you of
that.
What’s the difference between
these two types of motion?
Yes! The old car is moving slower than the other car! The change
in position of the slower car took a greater change in time.
But how fast is fast, and how
slow is slow?
• Let’s put numbers on fast and slow.
• Lets use a mathematical equation to
figure it out!
• How would you do it?
• Let’s call how fast or slow something
moves its speed.
• Speed is the change in position divided
by the change in time.
Lets write that mathematically!
• Speed = the change in position / the change in
time.
• That’s too long to write out for as many times
as we are going to use it. Our hands will ware
out.
• Lets abbreviate! Any suggestions?
• We need letters for speed, time, position, and
“the change in.”
• What would you choose?
S, x, & t
• The scientists in this country have chosen the
above. We will use those abbreviations too, so
we can communicate with the other scientists
across the country.
• S for speed
• x for position. Because x is the position
marker in math.
• t for time.
• But how should we represent “the change in?”
The change in.
Trace around, and the
sides keep changing!

Start here

•  is the Greek upper case letter delta.
• From now on,  will mean “the change
in”
• Actually, we will use the Greek alphabet
to represent several different terms in
physics. We do this because we have
more terms than there are upper and
lower case letters in the English alphabet.
Rewrite the equation.
• We can now write:
• Speed = The change in position /
The change in time
• As:
• S = x / t
• And that saves a lot of writing!
What does “the change in” mean
mathematically?
• Mathematically, the change in means:
• The final value – the initial value
• We can abbreviate this by putting a subscript f for
final and a subscript i, or 0 for initial. Like this:
• xf – xi , or xf – x0 , or tf – ti , or tf – t0.
• You will have to get use to using either i or 0 for
the initial value. The reason we use both is
because the starting value is the initial value, and
we often try to start at 0 to make the math easier.
How do we use this?
• The equation S = x / t can now be
written:
•S = (xf – xi ) / (tf – ti )
Yes, but how do we use this?
• Lets say you go from here to your
grandma’s house and it takes you 4
hours to get there. Lets also say its 200
miles to your grandma’s house. How
fast did you go? That is to say: How
much did you change your position in
that much time?
Step one.
• Write the equation.
• S = (xf – xi )/ (tf – ti )
• Step two:
• Solve the equation algebraically for the
unknown using only the lettered variables.
Do not use numbers yet! Except for 0.
• Step two is already done in this case. Except
that you can decide that xi, and ti are equal
to 0. So rewrite as:
• S = (xf – 0) / (tf - 0) so S = xf / tf
Step 3.
• Now plug in the numbers.
• What value should be substituted for the final
position (xf )?
• That’s right! 200 mi.
• What value should be substituted for the final time
(tf )?
• That’s right! 4 hrs.
• Rewrite the equation with the numbers:
• S = 200mi / 4 hrs
Step 4.
• Do the math!
• In this case we need to divide 200mi by 4hrs. 200
mi / 4 hrs. This, you should be able to do in your
head.
• If you use the calculator, remember the rule:
• The one on top gets punched in first!
• That is to say: Type in 200, then type the divided
by sign (÷), then type 4, then type the equal sign
(=), or return, or enter (depending on the
calculator).
• The answer in this case would be 50.
Step 5.
• We have one more step because the answer is not
just 50.
• 50 what?: Micrometers per nanosecond? Or did
we go 50 pounds to grandma’s house? Could we
have gone 50 acres to grandma’s house. Does it
make a difference?
• Yes it does!
• Step five: Include the units!
• In this case, the units are miles per hour. Since per
means to divide, we can write the units as mi /hr.
So the final answer is:
• S = 50 mi / hr
Let’s review.
• Step A – Write the givens, and unknowns.
• Step B – Write the base equation. Based on
the givens and unknowns
• Step C – Solve the equation for the unknown.
Don’t use numbers yet! (Except 0 in some
cases).
• Step D – Now plug in the numbers. Do the
math. Make sure your calculator is in the right
mode. Include the units! This helps you check
to see if you got the right answer.
Your turn!
• Solve these problems, and then share the answers.
• Travel 10 meters in 2 seconds. Find speed.
• Start at 5 meters, finish at 20 meters. When
starting your watch says 2 sec. When finished
your watch reads 5 sec. Find speed.
• You travel at a rate of fifty m/s for 40 s. How far
did you go?
• You travel at a rate of 100 m/s for 5000 m. How
much time did you spend traveling?
• S = 40 m/s. Initial time is 5 sec. Final time is 15
sec. Initial position is 30 meters from home. Find
your final position from home.