mr.p: Good morning.
Let's take a closer look
at Uniformly Accelerated Motion.
Bo: Hey, guys!
Billy: Hey, Bo. Bobby: Hi, Bo.
♫ (lyrics) Flipping physics ♫
mr.p: We've already begun working
with Uniformly Accelerated Motion or UAM,
and we have our four UAM equations.
Those are great, we're going to use those a lot,
however today I want to try to understand
what it means to have a uniform acceleration,
what it means to have a constant acceleration.
So let's start with the equation for acceleration.
Billy, what is the equation for acceleration?
Billy: Acceleration equals change in velocity
over change in time.
mr.p: Correct.
And, Bo, in base SI units,
what are the dimensions for acceleration?
Bo: Meters per second squared.
mr.p: Also correct.
We've learned that acceleration
is in meters per second squared,
however, I find the students better understand
what Uniformly Accelerated Motion means
when instead of using meters per second squared
we use meters per second every second,
which is the same thing
but is what acceleration means.
Meters per second every second.
In other words, if the acceleration of an object
is a constant 10 meters per second squared,
that means that the velocity of that object
is changing by 10 meters per second every second.
Let's take a look at a simple demonstration.
This is a basketball accelerating down an incline.
In order to make the numbers easy,
let's pretend the ball has an acceleration
of two meters per second every second.
The acceleration of the ball is actually
0.3287 meters per second every second,
however that number is unruly to work with
so we're going to use
two meters per second every second,
to make the numbers easier to understand.
So, what we're trying to understand is,
what does this mean?
The acceleration of the basketball is
two meters per second every second,
so, Bobby, what is the initial velocity of the ball?
Bobby: It looks like it isn't moving when you let go of it,
so the initial velocity is zero.
mr.p: Then, Billy, how fast is the ball
moving after one second?
Billy: Well, because the acceleration is constant
we can use the Uniformly Accelerated Motion equation,
velocity final equals... mr.p: Billy, please stop.
Remember, I'm trying to help you understand
what Uniformly Accelerated Motion means,
therefore we're going to put away
those UAM equations for a little bit.
Again, if the initial velocity of the ball is zero,
and it has an acceleration of
two meters per second every second,
what is the speed of the ball after one second?
Billy: Oh, its speed is increased
by two meters per second after one second,
so the ball is moving at two meters per second.
mr.p: Great! Now, one second later, at two seconds,
Bobby, how fast is the ball moving?
Bobby: It should be moving
two meters per second faster,
so two plus two is four meters per second.
mr.p: Yes! And at three, four and five seconds,
Bo, what is the speed of the ball?
Bo: Each second the speed increases
by two meters per second,
so six, eight and 10 meters per second
are the velocities.
mr.p: Absolutely!
That is what an acceleration
of two meters per second squared means,
it means the velocity is changing
by two meters per second every second.
Now, let's make a table out of this data.
The only data we are missing from our table
are the positions.
Let's assume the initial position is zero.
Billy, now you may use
a Uniformly Accelerated Motion equation
to determine all those positions.
Billy: We can use the UAM equation,
displacement equals velocity initial
times the change in time
plus one half times the acceleration
times the change in time squared.
The velocity initial is zero,
and the acceleration is two,
so the displacement then equals
the change in time squared.
So, one squared is one, two squared is four,
three squared is nine, four squared is 16,
and five squared is 25.
Those are all the positions in meters.
Bo: Hold up.
There's no way that ball moved 25 meters.
Billy: Remember, Bo,
two meters per second every second
is not the actual acceleration of the ball.
Bo: Oh, yeah, I forgot.
mr.p: Now let's try a slightly different example.
The initial velocity of the ball is now
10 meters per second to the left,
or negative 10 meters per second.
The acceleration of the ball is still
positive two meters per second every second.
So, Bo, what is the velocity of the ball
one second later?
Bo: Oh, well, it shouldn't matter
that the initial velocity is negative,
the acceleration is still a change in velocity
of two meters per second every second,
so we add two meters per second
to the negative 10 meters per second,
and the ball is now moving
at negative eight meters per second.
mr.p: Correct!
Now, Billy, what is the velocity of the ball
at each of the next four seconds?
Billy: Well, we continue to add
two meters per second every second,
so the velocities in meters per second should be
negative six, negative four, negative two, and zero.
mr.p: Yes! And again we can put
all these data in a table.
You can see I calculated all the positions
for the basketball, starting with an initial position
of 25 meters to match the final position
the ball was in during the previous example.
If you'd like to see those calculations,
they are in the lecture notes posted
on my website at flippingphysics.com.
I hope you now have a better understanding
of what it means for an object to have
Uniformly Accelerated Motion.
Thank you very much for learning with me today,
I enjoyed learning with you.