Bo: Hey guys!
Billy: Hey Bo! Bobby: Hi Bo!
♫ (lyrics) Flipping Physics ♫
Mr. P.: Ladies and gentle people,
the bell has rung therefore class has begun,
therefore you should be sitting on your seat
ready and excited to walk some graphs
a position as a function of time.
Bobby: Yeah.
Billy: Yes.
Bo: Okay.
Mr. P.: One of the things
that you're gonna be responsible to do in this class
is to be able to understand, interpret and draw
position as a function of time,
velocity as a function of time
and acceleration as a function of time graphs.
Today we're gonna work on
position as a function of time.
We'll get to velocity and acceleration
as a function of time
in a later lesson.
Let's start.
We're gonna draw a position as a function of time.
We're gonna deal with several graphs today
that have to do with position as a function of time.
We'll have position
on what we would normally call the Y axis,
and time on what we would normally call
the X axis.
Again, position in meters on the Y axis
and time in seconds on the X axis.
Let's just start with a single line
on our position as a function of time graph
which I've drawn here.
We're going to talk about the slope.
Bo, what's the symbol for slope?
Bo: The symbol for slope,
I don't think I remember.
Bobby: It's a lower case m.
Bo: That's right, thanks.
A lower case m.
Mr. P.: Great, the symbol for slope
is a lower case m.
Billy, what is the slope of a line?
Billy: The slope?
The slope of the line ...
The slope of the line is the rise of the line
over the run of the line.
Mr. P.: Very good, the definition of slope
is that it is the rise over run of a line.
In other words,
if you take a certain time period,
you will see that we have a certain run
during that time period
and we go through a certain amount of rise
during that time period.
The slope of the line
is if you take the rise during a certain time period
and divide it by the run
during that same time period.
Bobby, what's the equation for the slope of a line?
Bobby: y = mx + b.
Bo: Actually that's the slope intercept form
of a straight line equation.
Not the equation for slope.
Bobby: That's right.
The equation for slope ...
It's change in y over change in x.
Mr. P.: Very good.
Slope is equal to rise over run
it's also equal to the change in y over change in x.
But we don't have a Y axis
and we don't have an X axis.
We have instead of a Y axis, a position axis
instead of an X axis,
we have a time axis.
Instead of slope equals change in y over change in x,
it's gonna be the change in position
over the change in time.
In other words,
the slope of a position versus time graph
is equal to the change in position
over change in time.
Change in position over change in time.
That sounds really familiar.
Anybody have any idea what that is?
Come on!
We just defined this.
Class, what is change in position over change in time?
Bo: Velocity.
Bobby: Velocity.
Billy: That's right.
And displacement over change in time
is equal to velocity.
Mr. P.: One thing that you absolutely have to know
is that a slope of a position versus time graph
is velocity.
Again, the slope of a position versus time graph
is velocity.
What we're gonna do now
is I'm gonna draw a graph
of position as a function of time.
I'm gonna put a line on that graph
and I'm gonna ask a student to come forward
to be the object for that graph,
to walk that graph.
To walk the position as a function of time graph.
Let's actually start out by getting our bearings
and understanding where things are on the graph.
Here we go.
All right.
Everyone graph we're gonna walk in this class
is going to be done on the sidewalk
right out in front of my house.
We have to get our bearings.
If you are on the time axis,
you'll be standing on the sidewalk
right in front of the front door.
If instead you are below the time axis,
you will be to the left of the front door,
still on the sidewalk.
If you are above the time axis,
you will be to the right of the front door,
again, still on the sidewalk.
One more time.
If you are on the time axis,
you will be right in front of the front door.
If you are below the time axis,
you will be to the left of the front door.
And if you are above the time axis,
you will be to the right of the front door.
Let's draw our first line.
All right, this is our 1st graph.
One thing to make sure that we understand
when you start and stop please say "start"
right when you start walking
and "stop" when you are done walking the graph.
Billy, could you please give it a try.
Could you please start walking this graph.
Billy: You want me to go outside?
Mr. P.: Yes, please go outside
and give it a try.
Billy: Okay.
Start!
Mr. P.: No stop please.
Please don't walk across the street.
Bo: Dude, weren't you paying attention
when we learned about displacement.
Look both ways before you cross the street.
Bobby: And always cross corner to corner.
Mr. P.: Okay.
One common misconception with this graph
is because that the line is diagonal
that you must walk in a diagonal direction.
It's not true.
There is only 1 spacial dimension on this graph.
There is a time dimension
but only 1 spacial dimension
which means you should always be on the sidewalk.
It's just 1 linear dimension along the sidewalk.
Please give it a try again,
but this time stay completely on the sidewalk.
1 linear dimension.
Billy: Okay.
Start!
Stop!
Mr. P.: That's exactly it. Notice
he started to the left of the front door
and as his time went by,
he slowly went toward the front door
and then ended up to the right of the front door.
Just like it says on the graph.
Very nice.
Billy, why don't you come back inside?
Let's do the next graph.
Bo, could you please give this one a try?
Bo: Okay.
Start.
Stop.
Mr. P.: All right.
Let's talk about this one.
Billy, what did you think?
Did he walk the graph correctly.
Billy: Well, there is a line
so we should be moving.
Bobby: Actually if you look a the line,
as time goes by,
he's always in that same spot
just to the right of the front door.
He actually shouldn't move at all.
I think he did an excellent job.
Billy: Yeah and the slope of the line is 0
and the slope of a position versus time graph
is velocity,
therefore, his velocity should be 0,
therefore, he shouldn't move at all.
That makes sense.
Mr. P.: Very nice guys.
Bo, why don't you please come back in.
Let's do the next example.
Bobby, could you please give this one a try?
Bobby: Start!
Stop!
Mr. P.: Well class, how do you think he did?
Bo: I ain't got no beef with that.
Billy: Looks good to me.
Mr. P.: All right.
Then I have a question.
Was he facing the correct direction?
He was facing forward as he walked
but should he have actually been facing
the other direction and walked backward?
Bo: It doesn't matter.
Billy: The direction he should be facing
isn't indicated on the graph.
Mr. P.: That is correct.
There is nothing on the graph
that tells us the direction that he should be facing
only the way he should be moving.
The direction that he's going to go.
I have another question.
Other than the fact we can tell
he started to the right of the front door
and he ended to the left of the front door,
what's another way we can tell
from the line that he should be moving to the left?
Billy: Again, it's that the slope is velocity.
The slope of that line is negative
and therefore his velocity is negative
and to the left is negative.
Mr. P.: Absolutely!
Remember the slope of a position versus time graph
is velocity.
We went through and showed that before.
The slope of a position versus time graph is velocity.
This slope of this line
because the rise is actually negative
as time goes by,
that means this slope is negative.
Therefore, he should have a negative velocity,
negative slope, negative velocity
and a negative velocity is to the left.
Therefore, Bobby was absolutely right
to be walking to the left
or having a negative velocity, great!
Bobby, can you come back in?
Let's do one more graph.
Ryan, how about you give this one a try, please?
Bobby: I always love it when his kids help.
Bo: Yeah.
They sure know their physics too.
Billy: Glad, I don't have to give it a try.
Ryan: Start!
Stop!
Bobby: Excellent job, Ryan!
Mr. P.: The problem is
is that she actually did do something wrong
and we need to talk about it.
You could see in part 1.
Again in part 1, she started at the front door,
she walked to the right of the front door
and then for part 2 she paused for quite a while
and then for part 3 she moved
from to the right of the front door
to the left of the front door
but she did do something incorrectly.
What was it?
Billy: I don't think your kids can do anything wrong.
Bobby: I agree with Billy.
Bo: Me too, nothing wrong.
Mr. P.: Please, we all make mistakes.
Even me, come on.
Bobby: Velocity.
It's the slope again.
Notice that the slope in part 3
is actually greater than the slope in part 1
therefore, she needs to be moving faster in part 3.
Billy: Actually, because the slope
in part 1 is positive
and the slope in part 3 is negative,
technically the slope in part 1
is greater than the slope in part 3.
Mr. P.: That is true Billy,
however, I usually do it in terms of the magnitude
because it's easier to see there.
You could see the magnitude of the slope
or the magnitude of the velocity in part 1
is less than the magnitude of the slope
or the magnitude of velocity in part 3.
In other words,
the magnitudes of the velocity in part 3
is greater than the magnitude of the velocity in part 1.
In other words she should be moving faster
in part 3 than in part 1.
Great.
Ryan, could you do it one more time
but this time do it correctly please.
Ryan: Start!
Stop!
Mr. P.: Another way to look at this
is that in part 1,
she had a large amount of time
to go through a short distance
whereas in part 3 she had a short amount of time
to go a large distance.
In other words,
she needs to move faster in part 3
than she does in part 1.
You could clearly see
from the example problems that I've done,
it is very important to remember
that the slope of a position as a function of time graph
is velocity.
Please remember that.
Ladies and gentlepeople,
I enjoyed learning with you today.
I hope that you enjoyed learning with me.
Voiceover: Lecture notes
are available at FlippingPhysics.com.
Please enjoy lecture notes responsibly.