Bo: Hey, guys.
Billy: Hey, Bo. Bobby: Hi, Bo.
♫ (lyrics) Flipping Physics ♫
Mr. P.: Ladies and gentlepeople,
the bell has rung,
therefore class has begun,
therefore you should be seated in your seat
ready and excited to learn about
velocity and speed.
Billy: Velocity.
Bobby: Speed.
Mr. P.: All right, let's get started.
The symbol for velocity is a lower case v.
In order to get the equation for velocity,
I need the symbol for displacement.
Bo, what's the symbol for displacement?
Bo: Delta x.
Mr. P.: Yes, the symbol for displacement
is delta x; therefore, the equation
for velocity is ... velocity equals delta x
over delta t.
Billy, remind me what does delta mean?
Billy: Delta means change in.
Mr. P.: And Bobby, what does x mean?
Bobby: X means position.
Bo: And not distance.
Mr. P.: Therefore, the equation for velocity
can be read as velocity equals the change in position
over the change in time.
Bo, remind me what equation does delta,
or change in mean?
Bo: Delta represents final minus initial
in an equation; therefore, delta x means
position final minus position initial.
Mr. P.: Correct. Then in the numerator
of the fraction we have position final
minus position initial.
Billy: Then in the denominator we have
t f minus t i, right?
Mr. P.: Aaah! Aaah! Eeh! Okay, so y'all have this tendency
to say the letters and not what the variables mean.
It is very important that you say
what the variables mean.
The more you actually say the variables,
the more we say it,
the more we understand it,
the more we're actually thinking about
what it means rather than just
these random letters.
That's very, very important.
Billy, could you please try again?
Billy: Delta t, or change in time,
means time final minus time initial.
Mr. P.: Yes. So the complete equation then
is velocity equals displacement
over the change in time,
or the change in position over change in time,
and delta means change in; therefore,
it's going to be the velocity is equal to
position final minus the position initial
divided by the quantity time final
minus time initial.
Remind me, class, what 2 things does displacement
have that we need to remember?
Bobby: Direction and magnitude.
Billy: That's right.
Displacement has both magnitude and direction,
and distance has magnitude only
and no direction.
Mr. P.: This means that because velocity
is in terms of displacement,
that velocity is also going to have
both magnitude and direction.
Again, velocity has both magnitude and direction.
Very important.
All right, let's go through an example problem,
but before we even go through that example problem,
we're actually going to first talk
about translating problems.
In physics you often have to take the words
and translate them into physics,
and so we're going to do this over and over again
in this class.
We're going to start out by
today we're going to read the problem,
and then we'll work together to translate
the problem into physics.
Now, Bobby, if you could please read
through the problem.
Bobby: Mr. P. takes his dog, Buster, for a walk.
If they walk for 27 minutes
and travel 1.89 kilometers east,
what is their average velocity
in meters per second?
Mr. P.: Great. Now that we've read
through the problem once,
we're actually going to read
through the problem slowly,
and I'm going to ask you to pause
so that I can write stuff down.
So go ahead.
Bobby: Okay. Mr. P. takes Buster for a walk.
If they walk for 27 minutes,
Mr. P.: Okay, please stop.
Billy, some variable equals the 27 minutes.
Please tell me what variable is equal to 27 minutes.
Billy: That would be time.
Mr. P.: Which one? Initial or final time?
Billy: Actually, neither.
It would be the change in time.
Mr. P.: Very nice.
Delta t or the change in time
is equal to 27 minutes.
Notice that's not a specific time,
but rather a change in time,
a time duration.
It's not like 9:16 AM which would be a specific time.
Bobby, please continue.
Bobby: And travels 1.89 kilometers east.
Mr. P.: Please stop.
Bo, what variable equals 1.89 kilometers?
Bo: Displacement.
No, distance.
No. No, it's displacement. Displacement.
Mr.P.: Bo, I do agree it should be displacement.
However, the way I've written it on the board
is actually just distance.
Bobby, could you please fix it?
Bobby: You need to give it a direction
so just add an east, right?
1.89 kilometers east.
Mr. P: Bobby, please continue.
Bobby: What is their average velocity
in meters per second?
Mr. P.: So then I write v sub avg
is equal to "?" so that we have the average velocity
is equal to "?" illustrating what we're trying to find.
Also, I write, I add meters per second
parenthetically after the "?"
to illustrate that we're looking for
the average velocity in meters per second.
Bo, what do we want to do next?
Bo: So the average velocity equals 27 minutes,
yeah, divided by 1.89 kilometers.
Mr. P.: Aaah! Aaah!
Bobby: You are skipping steps.
Billy: Falling down the stairs.
Bobby: You're going to hurt yourself.
Billy: And get it wrong like you currently are.
Bo: Ah, start with an equation.
Mr. P.: Yes, please show every step.
Don't skip steps.
Bo: Okay, I'll try again.
Average velocity equation.
Average velocity equals displacement over time.
We know the displacement is 1.89 kilometers
so write that in for the change of position.
The change in time is 27 minutes
so write that in for delta t.
Mr. P.: Great. Please notice that this is
much less painful and is actually correct so far.
We do have the average velocity
in kilometers per minute.
We're looking for it in meters per second.
Billy, could you please convert
to meters per second.
Billy: There are 1,000 meters in 1 kilometer
so I'll multiply by 1,000 meters over 1 kilometer
so that the kilometers cancel out,
and there are 60 seconds in 1 minute
so multiply by 1 minute over 60 seconds
so the minutes cancel out,
and we are left with meters per second.
Mr. P.: Correct. We multiply by 1,000 meters
over 1 kilometer; therefore,
the kilometers cancel out.
We multiply by 1 minute over 60 seconds;
therefore, the minutes cancel out,
and we're left with meters per second.
What do we get for an unrounded answer please?
It's 1.166, well a repeating 6.
Great, and what Bo, is our final answer?
Bo: Because 27 minutes only had
2 significant digits,
your average velocity was 1.2 meters per second.
Bobby: Don't forget direction.
Bo: 1.2 meters per second east.
Thanks, Bobby.
Mr. P.: Great. Our final answer
for our velocity which has both magnitude
and direction is 1.2 meters per second,
1.2 would be the correct number of sig figs with 2.
1.2 meters per second would be the magnitude,
and east would be the direction.
Now we need to take a moment to talk
about speed.
Bo: Hold up. Hold up. I have a question.
Why didn't we use position final
minus position intial,
or time final minus time initial?
Billy: I also have a question.
Why didn't we convert first
before using the equation for velocity?
Mr. P.: Okay, we didn't need to use position final
minus position initial,
or time final minus time initial
because of what we were given in the problem.
We knew the change of time.
We knew the change of position
or the displacement.
Those were just given.
We might run across a problem at some point
where we know the time final and time initial,
and we can then figure out the change in time.
Same is true for the position final
and position initial,
but because of the way this problem was phrased
we didn't need to use the second half
of the equation here, position final
minus position initial divided
by time final minus time initial.
As far as whether we could have converted first.
Absolutely, you could convert first.
It doesn't really matter.
There will be times when you will need
to convert the dimensions first,
and we'll talk about those more when we get there.
But regardless, it wouldn't matter.
You're going to get the exact same thing
whether you convert the dimensions first,
or you convert them in the equation itself.
Any other questions?
Billy: Not yet.
Mr. P: Great. Now let's take a moment
and talk about speed.
Let me write down the equation for speed.
The equation for speed is speed equals
distance over time.
Again, speed equals distance over time.
Generally I like to write out all the words,
the letters in the words there
rather than using variables.
Unfortunately, by time in this equation,
we actually do mean time duration.
That's 1 of the reasons I like to write
the full T-I-M-E time rather than lowercase t
which would just represent a specific time.
So this is the time duration.
Notice that speed uses distance
and not displacement.
This is an important distinction
because displacement, class, has both ...
Class: Magnitude and direction.
Mr. P.: And distance has ...
Class: Only magnitude.
Bobby: And no direction.
Mr. P.: Therefore, class, speed has ...
Class: Only magnitude.
Bobby: And no direction.
Mr. P.: Very good.
Speed has magnitude only.
It does not have direction.
Just like distance has magnitude only
and no direction; therefore,
class, are speed and velocity the same thing?
Bobby: No.
Bo: Nope.
Billy: No, clearly not.
Mr. P.: Correct.
Velocity does not equal speed.
In this particular case,
in the problem we just went through,
the magnitude of the velocity actually
is going to have the same magnitude
as the speed.
Why in this particular case is that true? Bo?
Bo: Isn't that always true?
Bobby: I don't know.
Billy: It can only be true when the object
moves in a straight line.
Mr. P.: Yes.
The speed and velocity only have
the same magnitude when you're moving
in a straight line.
Bo: Oh, yeah.
That's because speed is in terms of distance.
Billy: And velocity is in terms of displacement.
Bobby: Makes sense to me.
Mr. P.: Very nice.
Sounds like you've been paying close attention
which is always so helpful.
So ends my introduction to velocity
and the differences between velocity and speed.
I hope you enjoyed learning with me today.
I enjoyed learning with you.
Lecture notes are available
at FlippingPhysics.com.
Please enjoy lecture notes responsibly.
Mr. P.: Velocity equal, huh, Billy ...
Remind me, Billy what does velocity mean?
No.
Billy, remind me what does velocity ...
Therefore, the equation for velo- ...
Correct, in the Newman a.
Aah, aah. Ha ha. Hee. Ha ha ha ha.
Actually that's a lie.
Ah, Bob, [unintelligible]
I add m over s. No.
Great. Our final, brrh.
Where that will come along when we need to ...
Where am I going?
Ah.