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 do a basic example problem
about acceleration and to understand a little bit
about the direction for acceleration.
Bo: Ready Bobby: Set. Billy: Go!
Mr. P: Okay, here we go.
Billy, please read the problem.
Billy: Mr. P is riding his bike
at -14.3 kilometers per hour when he begins pedalling
the bike to cause a constant acceleration.
If, after 6.4 seconds,
the bike is moving at -23.7 kilometers per hour
what was the acceleration of the bike?
Bobby: Uh, can you show that again please?
That happened pretty fast.
Mr. P: For you Bobby, yes.
Great. Now let's translate the problem to physics.
Billy, if you could please read again,
and Bo, could you please do the translation?
Billy: Mr. P is riding his bike at -14.3 kilometers per hour
when he begins pedaling ...
Bo: Please, stop.
The velocity initial is -14.3 kilometers per hour.
Billy: Pedaling the bike to cause a constant acceleration.
If after 6.4 seconds,
the bike is moving at -23.7 kilometers per hour
what was the acceleration of the bike?
Bo: The change in time is 6.4 seconds,
the final velocity is -23.7 kilometers per hour,
and acceleration equals question mark
because acceleration is what we're trying to find.
Mr. P: Bobby, what next?
Bobby: Well, we learned last time
that kilometers per hour and seconds don't match very well,
so let's convert both of the velocities
to meters per second.
We know there are 3,600 seconds in an hour,
so multiply both velocities by 1 hour
over 3,600 seconds to cancel out the hours.
We also know that there are 1,000 meters
in 1 kilometer so multipy
both velocities by 1000 meters over 1 meter
to cancel out the kilometers.
Mr. P: What do we get then for numbers for velocity initial and velocity final?
Bobby: I actually have both answers.
The initial velocity is -3.972,
and the 2 is repeating,
and the final velocity is -6.583
with a repeating 3.
Mr. P.: Great. Bo, what should we do now?
Bo: Again, we start with the equation.
Billy & Bobby: The equation.
Bo: Yes, the equation.
Acceleration equals the change in velocity
over the change in time
where the change in velocity is equal to
velocity final minus velocity initial.
Once we have the whole equation written down,
we can just plug in all the numbers
because we have the numbers,
and we get - 6.5833333 minus a -3.9722222.
That whole quantity divided by 6.4.
Mr. P.: Yes, it is that simple,
and what do we get for numbers?
Bobby: That worked out to be -0.4079861,
with 2 sig figs that would be
-0.41 meters per second squared.
Mr. P.: Yup, we get -0.41 meters per second squared,
2 sig figs because of the 6.4 seconds.
Questions?
Bo: I have 1.
Bobby: Actually, I have 1 too,
but you can go first.
Bo: Thanks, Bobby.
In the video, the velocities weren't actually negative.
Why not?
Mr. P.: Oh, yeah. Good eye, Bo.
You're talking about the number shown
on the bike, right?
Bo: Yup.
Mr. P.: Well, okay, Billy what is the name
of the item on the bike that is showing
the number, 23.7 kilometers per hour?
Billy: I think it's called a speedometer.
Mr. P.: Correct. We're reading that 23.7 kilometers
per hour and the 14.3 kilometers per hour
off of the speedometer on the bike.
Notice it's a speedometer not a velocitometer.
A speedometer not a velocitometer
or whatever it would be called
displays just the speed not the velocity.
So in this particular case,
it's giving us the magnitude of the velocity
at that particular time.
So the magnitude of velocity at this particular time
is going to be the speed and not the velocity.
Now we do know it's negative
because I'm moving to the left in the video.
Bo: Okay, yeah, that makes sense. Thanks.
Bobby, what was your question?
Bobby: My question had to do with the fact
that the bike is speeding up,
and if the bike is speeding up,
shouldn't the acceleration be positive?
I thought that negative accelerations meant
that you were slowing down.
Mr. P.: Oh, yeah, the direction,
I guess we should talk about that.
It is in the title of the video.
First off, realize that we did do
the problem correctly.
We should end up with a negative acceleration
even though we're speeding up.
Let's talk through why that is
by way of some examples.
Billy: Okay.
Bobby: Good. Let's do that.
Mr. P.: Okay, let's say by way of an example
that I'm riding my bike to the right
and speeding up.
In this particular case,
that would mean that my velocity would be to the right,
and my acceleration would also be to the right
and both would be positive
because they would be to the right.
If instead I'm riding my bike to the right
and slowing down,
my velocity again is going to be to the right
and positive; however, my acceleration
is going to be to the left and negative.
Billy: Oh, in other words,
when you are speeding up,
the acceleration is in the same direction
as the velocity.
Bobby: And when you're slowing down,
then the velocity and acceleration are
in opposite directions.
Mr. P.: Exactly. If the object is speeding up
that means that the velocity and acceleration
are both going to be in the same direction.
However, if the object is slowing down,
that means that the velocity and acceleration
are going to be in opposite directions
which means if I am riding my bike to the left
and speeding up,
then because I'm riding my bike to the left,
the velocity is going to be to the left and negative.
If I'm speeding up then my acceleration
is going to be in the same direction
as the velocity which is going to be
to the left and negative.
If however I am riding my bike to the left and slowing down,
that means that my velocity is still
going to be to the left and negative.
However, because I'm slowing down
the acceleration is going to be opposite
of the direction of the velocity.
And, therefore, the acceleration is going to be
to the right and positive.
Bobby: Thanks.
Mr. P.: Now I do think that that bears repeating,
and writing down on the board.
Again, if the object is speeding up,
the velocity and acceleration are
in the same direction,
and if the object is slowing down,
the velocity and acceleration are
in opposite directions.
Let's take 1 more look at the 4 examples
because, darn it, it took me a long time to film.
Well, any more questions?
Bobby: Nope. Billy: No.
Bobby: Thanks.
Mr. P.: Actually, I'm a bit surprised that
there aren't any more questions
because if you look at our acceleration,
this is our answer for acceleration; however,
it doesn't have a direction,
and acceleration has both magnitude and direction.
Unfortunately, because of the problem statement
we didn't know enough to be able to figure out
a direction from the problem.
I kind of did this on purpose
because you're going to run into problems
where you're not given a direction,
and alas you can't actually figure out a direction
in your answer and this is
what you're going to need to do.
So I thought it would be good to go
through an example like that although in the problem
they probably should have said something
about direction so that you could figure out
the direction for your answer
because, again acceleration has
both magnitude and direction.
There you go.
Ladies and gentlepeople,
I enjoyed learning with you today.
I hope you enjoyed learning with me.
Voiceover: Lecture notes are available
at FlippingPhysics.com.
Please enjoy lecture notes responsibly.
Voiceover: You can both film at the same time.
Child: Yeah.
Mr. P.: Hold this.
Child: I don't know how to work this one.
Mr. P.: It's the same one.
So move forward and stand about here,
and I want you to film what mommy and I
are going to do.
Child: So do you hold it like this?
Mr. P.: Yup, well you can see what you're filming.
Child: Well, I can't get the whole car.
When do I press record?
It is recording right now.
I'm filming you.
Child: No, you're not supposed to be.
Child: I'm not filming
I don't know how.
Child: I got some video.
When do I press record?
Mr. P.: So what I'll do is I'll yell 3, 2, 1, brake.
I'll go over to the other side.
So we're going to do the same thing
only I'm going to be on this side of you now.
Why don't we head back.
I'm going to take some wearing the chest harness.