Hi. It’s Mr. Andersen and this AP Physics essentials video 59. It is on position, velocity
and acceleration. And in this video I am going to show you how to measure the position, determine
the velocity and then determine the acceleration. And if you want to feel that acceleration
then you should jump out of an airplane. And what is going to happen, your position is
going to change over time. It is going to get more and more negative, as your velocity
increases in the negative, because you are accelerating. Now eventually you will reach
terminal velocity where the force down of gravity equals the force of air resistance.
It is over 100 miles per hour, but it is hard to see that in this video because the camera
man was traveling with the skydivers. They have the same frame of reference. And so if
you really want to measure position, velocity and acceleration, you have to remove yourself
from that setting and then do some detail studies to figure out what is really going
on. And so if we take a position of an object, and here I have marked the center of mass,
and we watch how it changes over time, so its position at point 1 and 2 and 3. Now you
can see that the time between each of those positions is the same, so its displacement
is increasing towards the right. Its position is changing towards the right. That displacement
is a vector towards the right. Now the displacement divided by the time is going to give us a
velocity. And the velocity is a vector to the right as well. So if you think about it,
since the time was the same between here and here, and then between here and here, we know
the velocity is greater here because it is a greater displacement for a given period
of time. Now how do we measure the change in velocity? Well the velocity divided by
time is equal to the acceleration. And so if we ever have acceleration we know that
there is a net force acting on that object or acting on that center of mass and that
the acceleration and the net force will always be acting in the same direction. So if we
see acceleration we know there is a net force at play. And so one thing you should be able
to do right away is look at a position versus time graph and figure out is acceleration
occurring or not? And so we have an object right here, I have marked the center of mass
right in the middle, and what I am going to do is let time progress and I am going to
graph the position over time. Now this object is not moving. And so what would the position
versus time graph look like? It is going to look like this. In other words its position
is not changing over time. And so it is going to be a straight line and it is also going
to be a straight horizontal line that has no slope. And because it has no velocity,
it has no speed. And so is there a net force acting on it? No. It is just sitting there.
There is no change in its velocity so there is no net force. Now let me show you another
object. This object is going to have constant velocity. So it is always moving to the right
and it always has the same velocity. So what would the graph of that object look like?
Well it is going to be a straight line but it is going to have a straight line that has
a positive slope or it is moving towards the right. And so at any point along this line
it has the same exact velocity. And what we can do is we can measure the slope of this
line and it would tell us the velocity at that point which is the same throughout that
whole time. Now what would it look like if we have an object that is accelerating? And
so you should kind of make a guess at this. But now we have an object that is going slow
and now it is getting faster and faster. So what would the curve look like? It is going
to look like this. And so that velocity is increasing and so we are seeing a slope at
the bottom of almost zero, it is not going anywhere but then as we move far to the right
it has a really high velocity. And so that is an accelerating object so there must be
a net force that is acting on it. And I wanted to measure this. And so I used a piece of
software called video physics and my phone and I just went out and filmed a few things.
And here I have a car. And what I have done is set up the scales, so it is 2 meters from
here to here. I set the origin right here at the center of mass of the car. And so I
set that in the program. And then I just simply filmed it and I marked the center of mass.
And you can see that I was not perfect, but the center of mass is moving an equal amount
over a given time. And so what does that mean? If we graph it we are going to have a position
versus time graph that looks like this. And so we are seeing each of these, this the time
on the x-axis and the position of the y-axis, and so what we have is a straight line. So
what does that mean? We have a velocity that is constant. So it is moving with a constant
velocity to the right. Now we can take a graph like this and we can actually figure out the
speed of that car. So the slope of that line, if it is about a 5 meter rise and a 0.7 second
run, I just divid 5 by 0.7 and I get a velocity of around 7 meters per second using significant
digits. And so that is around 20 miles per hour. And so it is constant. It is moving
with constant velocity to the right. So what is the acceleration of the car? Well since
the velocity here and here and here is always the same. It is never changing. We have an
acceleration equal to 0. And so that means if this object has a center of mass there
is no net force acting on the car. Now are there forces acting on the car? For sure.
There is friction and air resistance slowing it down. And then there is the actual ground
pushing on it, the wheels that are moving it to the right, but they are all equal. So
those are balanced net forces and so there is no acceleration. Let me show you what acceleration
look like. So I took a basketball and did the same thing. I measured and set the scale
of the basketball and then I just dropped it and marked that center of mass as it fell.
And so what is the curve going to look like? Well it looks like this. And so we have, I
set the origin right here at 0. And so in those first little bits of time it is not
moving very far at all. But we can see that it is accelerating or the velocity is getting
greater and greater in the negative. And so we are increasing the velocity over time.
We know that acceleration is at play. Now how could you figure out the velocity at any
point along here? We just figure out the slope right here of this line and that would tell
me the velocity. You can see the slope right at the beginning is 0, but we are going to
have a greater velocity as we approach the bottom of the curve. And so the velocity is
increasing in the negative, so how do I figure out what the acceleration is? Well what I
then did is graph the velocity versus time. So now we have a velocity of 0 to start with
and then we see an increasing velocity as the ball falls farther down. And so you can
see that that is a straight line. And so what I can do is I can calculate the slope of that
line, the slope of the velocity versus time graph and that is going to give me the acceleration.
And so we see around a negative 5 meter per second change over about 0.5 second as I measure
this. And so we simply divide one by the other and I have an acceleration of around negative
10 meters per second squared. Now you know the acceleration due to gravity is negative
9.8 and so I am pretty close just using this crude software. And so is there a net force
acting on that ball? Sure. It is going to be in the negative direction. Now there might
be some air resistance in the opposite direction, but at this point, until we have too much
air resistance, until we reach that terminal velocity, there is a net force down and that
is why we have a net acceleration in the negative value. And so did you learn to make predictions
about acceleration and velocity of an object? Could you look at data and figure out if an
object has a velocity and if so is it a change in velocity? Is it accelerating over time?
And then finally could you use mathematical models or analyze graphical relationships
to figure out the position, the velocity and the acceleration? Again I used video analysis.
In a physics lab you could use a ticker tape or you could use a motion sensor to do it.
I hope that made sense. And I hope that was helpful.