This video is about making position time graphs. Position time graphs show an
object's position on the y-axis and the time on the x-axis. They're used to show
complicated motion on a simple picture. So as an example this graph represents
the position of an object after a certain amount of time has passed. So I'm
going to drop an object here (a person) and I'm going to say that this person is
starting at a position of 3. So when no time has passed yet they're at a
position of 3, so that would mean that my y intercept of the graph when time is
equal to 0 is going to be a position of 3. I'm now going to allow time to pass,
and you're going to observe how that affects the position graph as the person
moves. So you can see that they moved from a position of 3 to a position of 6
and it took them 3 seconds, so that means they're moving up one unit of position
for every second that passes, and you can see that's reflected on the graph. For
every 1 second that passes they're up another one unit of position on the
graph. For this next part of the graph they're going to be stopped, and this is
what that looks like. You can see they're just staying at the same position as the
time passes, and they'll move like this, and then like this. So I'm gonna have you
watch a few of these and begin to pick up on any patterns that you notice in
how the graph works. Here's another example. So we're just going to observe
how the person moves, and watch what it does to the position time graph.
Okay now that you've had a few examples of those graphs, I'm gonna play an
animation and have you try to guess what the graph is going to look like for this
specific animation. So I'm going to start this person off at a position of 2 and
then run the clock, and I'm going to play this a few times so you have a chance to
draw this in your notes and see if you can guess what the position time graph
will look like. So we're going to start now.
And I can replay that one more time.
Okay here's the answer. This is what it's going to look like. They're starting at a
position of 2 so that means that the y-intercept of the graph is going to be
at 2. They then move up at 1 meter for every second that passes until they
get to a position of 6, and then they stop for 5 seconds and then they move
down at 2 units of position for every second until they're at a position of
0 at 12 seconds. So that's what that graph would look like. We can now begin
to pick up on patterns in these graphs. The first one you might have noticed is
that the y-intercept of a position time graph is the starting position of the
object. This is always true because by definition, the y-intercept is what the
y-value is doing when the x-value is 0. So here this is what the position is
doing when the time is 0, which is the starting position of the object. The
slope of the graph is equal to the velocity of the object. The reason why
this is the case is because if you look at the rise and the run, I can see that
the rise is the change in position which is the displacement, and the run is the
change in time, and because slope is rise over run I can rewrite that as the
displacement over the time, which is equal to the velocity. So this will
always be true. The slope of the position time graph is always going to be equal
to the velocity because of this definition. So I can look through this
graph here and just observe what's happening for this first section. I can
see that this person is moving at 1 meter per second because they have a
slope of 4 over 4 (a rise of 4 meters and a run of 4 seconds) so their velocity is
1 meter per second. So for every 1 second they travel exactly 1 meter. In this next
section I can see that this is just a flat line, so the position is not
changing at all, so that means that the slope is 0 over 5 which is just 0 meters
per second and that means that their velocity is 0, and you could see also
that they weren't moving in that period of time, they were just standing still, so
they have a velocity of 0. For this last section I can see that they're moving
down six meters in three seconds so that means that their velocity here is
negative 2 meters per second (6 divided by 3) and I can see here also that when they move down they're moving down 2 meters for every 1 second
that passes. So that's a really important pattern in position time graphs that we
can use to help us draw and interpret them. Here's an example problem: what is
the starting position of this object and what is the velocity of this object?
Well the starting position is pretty easy, that's just the y-intercept so
that's just going to be 2 meters. The velocity is a little bit more difficult.
We just need to take the slope for that. So the run here is 12 seconds, the rise
is 3 meters, so the slope is going to be 3 meters divided by 12 seconds
which is equal to 0.25 meters per second, so that would be the velocity of the
object on this position time graph. We can also determine the starting position
of this object and also determine the velocity at 2 seconds the velocity at 6
seconds and the velocity at 10 seconds the starting position here is 4. That's
pretty simple. I'm now going to look up at what's going on at 2 seconds, and I
can see here that the line that this is on has a run of 4 seconds and a rise of
2 meters so that means that the slope at that point is 2 meters over 4 seconds
which is equal to 0.5 meters per second. Over here this line I can see is
perfectly flat so that means that the slope is just 0, it's 4 seconds long but
it's not going up or down at all so it's 0 over 4 so the velocity there is 0
meters per second. Finally at a time of 10 I can see that this line that it's on
has a run of 4 and a rise of -6 so I plug those in and I get a velocity
of -1.5. So that's how you would find the velocity at different times for
an object on a position-time graph. This next section is about how to find the
distance and displacement on a position time graph. To find the distance you're
just going to add up all the individual distances that this object travels along
its path, and to find the displacement you're just going to compare the
beginning and final points that the object is at. So you can
see for this object that they're going up 4 meters and then they're standing
still and then they're going down 6 meters like this, so the total distance
here would be 4 plus 0 plus 6 so the total distance would be 10 meters,
and the displacement we just have to compare the beginning and ending points
so they're ending at a position of 0 and they started at a position of 2, so
their displacement is just going to be -2 meters specifically. That's
how you find the distance and displacement on a position-time graph.
Here's another example: what is the distance the object traveled after 7
seconds and what is the displacement it traveled after 7 seconds? So let's
compare those 2. I can see that the total distance traveled here is going
from 1 to 7 so that's a distance of positive 6. It then stay still, so we
don't add any distance there, and then it goes down to 7 seconds so I can see
that it traveled another 5 meters, so the total distance it traveled was
11 meters. The displacement is just the straight line length from where it
started to where it stopped, so it's started at a position of 1,
ended at a position of 2, so the displacement is plus 1 meters.