—
Mr. Andersen shows you how to interpret a position vs. time graph for an object with constant velocity. The slope of the line is used to find the velocity. A phet simulation is also included.
—
—
Transcript Provided by YouTube:
00:00
00:07
Hi. This is Mr. Andersen and today I am going to be talking about position versus time graphs.
00:11
First thing you should know is that this is part 1. I’ll also do a part 2 on position
00:17
versus time. Part 1 I’m going to talk about objects that have constant velocity. And in
00:22
the next, part 2 we’ll talk about acceleration, deceleration. And so if you’re in the wrong
00:27
spot make sure you start where you should. Now what do I mean start? This whole unit
00:34
on position versus time graph and graphing in general is designed so that, let me graph
00:41
out a quick one. That. And then let’s say like this. And let’s say it goes like this.
00:54
So the whole thing is designed so that when you are done with this unit on graphing you
01:04
should be able to take a graph like this and know that’s not super great. But you should
01:09
be able to take a graph like this, a position versus time graph. And just looking at it,
01:13
you should be able to figure out exactly what this object is doing. Not only should you
01:18
be able to figure out what the object is doing you should be able to go from a position versus
01:21
time graph to a velocity versus time graph. And then from a velocity versus time graph
01:26
to an acceleration versus time graph. In other words it has taken me a long time to do this.
01:31
But I can literally draw it. So if I say this is the origin. So we say this is a velocity
01:36
of 0, I can look at this little unit here and I can figure out that it’s going to have
01:40
a velocity of like that. And then it’s going to have a velocity of like that. And then
01:49
the velocity is going to go like that. And if you don’t know how to do that, like that,
02:01
then you’re in the right spot. Because we’re going to start right here. If you do know
02:05
how to do that, and then to go from here to an acceleration graph, then don’t watch these
02:09
videos because you clearly know what’s going on. So let me clear that off. I’m sorry. I
02:12
got a little into that. And let’s get started. Best place to start is with The Moving Man.
02:18
Now what is The Moving Man? The Moving Man is a simulation that was created at the University
02:23
of Colorado. And what they do is they move a man about and you can actually start to
02:29
play around with position versus time graph. And so if you’re struggling with this, please
02:32
go there. And even if you’re not, please go there. And that’s what we’re going to do as
02:37
well. So here’s The Moving Man. And if I hit play at the bottom. Now I’ve pared it down
02:42
so I really only have the simplest things. You also could have velocity and acceleration.
02:47
But since this is position versus time I’m just going to start there. And so I’ve hit
02:52
play. And what we can see that our man is not moving. And so our graph keeps him right
02:57
at 0. Okay. So that’s kind of boring. So let me clear that again. And let’s play it again.
03:02
So what you can do is I can input the man’s position. So I’m going to move the man to
03:07
5. And what you see is the man up here quickly moves to position 5. And you can see that
03:13
reflected in the graph down here. So let’s move him to negative 5. Or let’s move him
03:19
to 8. Or let’s move him to 6. Or let’s move him to negative 8. Okay. So if I pause it
03:29
right here, let’s look, and you can hit play back and then we can watch happened. And so
03:34
for the first period of time he was at position 0. And then he quickly moves to position 5.
03:40
And so what a position versus time graph really tells us is where he is. Or she is. He then
03:46
quickly moves back into the negative. And then back into the positive. And then a little
03:52
less positive. And then finally moves into the negative again. And so if you see a position
03:59
graph like this, position is always going to be x graphed on the y-axis. And time is
04:04
always going to be graph on the x-axis. If you see your graph like this, it simply is
04:09
a man positioning himself in different positions. Now it’s a little unrealistic. In other words
04:15
we can not move that quickly. And so let me move him back to position 0 and show you what
04:21
might look a little bit more like it. So let me play it again. And what I’m going to do
04:26
is use this dragger to actually move him in a natural fashion. And so let me try to move
04:30
him in a natural fashion to position 5. And then let him rest there for a little bit.
04:37
Now let’s move him back to maybe position 1. And then way down here very quickly into
04:47
it looks like position negative 4.5. And then let’s have him rapidly go up here at the end.
04:53
Okay. Now let’s watch that. Because I was controlling it so it was hard for me to watch.
04:57
So let’s watch what happens. So there’s a long period of time when the man is not moving.
05:05
But then the man moved from position 0 to position 5. And so that should be a straight
05:11
line when I was trying to do it. And so what that straight line indicates, let’s try to
05:14
go back and see if we can see that again. Let’s watch his behavior as he goes. It’s
05:21
a little jerky. But you can see that the man is moving. And since this is a straight line
05:27
the man should be moving at a constant velocity. Or in other words he’s not accelerating. Let’s
05:32
watch again. Okay. Now the man moves back. So the man moves back to this position like
05:41
position 1. And the speed here, let’s go look at that. So the speed of the man’s movement
05:47
right here, watch how fast he’s moving. And the speed of the man’s movement over here,
05:55
let’s go way back here again, is constant. And so what does this mean when the line is
06:02
moving up? It just means that the man is moving to the right. And what does it mean when the
06:07
line is moving down. It means the man is moving to the left. Now this line looks a little
06:13
bit steeper, so let’s watch what happens. Can you see how the man is moving faster?
06:17
And now let’s watch the man at the end. The man, whoa, really moved. And so the slope
06:24
of this line also tells us the speed. And so that’s the first rule. The first rule that
06:29
you should pick up, at least that I’ve picked up is that the slope equals the velocity.
06:43
And if there’s no slope, so if slope equals 0, then the man is not moving at all. So here.
06:52
If the slope is negative, then the velocity is negative. And it doesn’t mean that it’s
06:56
somehow going slower. It just means that its moving in the opposite direction. So it’s
07:00
moving down like that. And so that’s what you can learn from Moving Man. You can move
07:05
it back and forth. And you can try to figure out what position versus time graph is. Now
07:09
on our test we don’t have to play with Moving Man. On our test we have to solve problems.
07:14
And so let’s get to some actual problems. So what do we have here. Now we’re not given
07:18
the man but we’re given the position versus time graph. And so knowing what you now know,
07:24
what is this mean? Well first of all it’s a slope. It’s a positive slope. And that means
07:32
the man is moving. Where does the man start? At position 0 and time 0. And where does the
07:37
man end? At position 6 and at time 3. So what did the man do from here to here? The man
07:44
walked. And walked with a constant velocity. Now the cool thing is that we can actually
07:49
use the slope of this line to figure out how fast the man is walking. So what’s the rise
07:56
in this? Well it goes from 0 to 6. And so the rise is going to be 6 meters. What’s the
08:02
run? It goes from 0 to 3. And so that’s going to be 3 seconds. And so the velocity in this
08:08
case is actually 6 meters per 3 seconds. Or 2 meters per second. Now we learned in the
08:16
last podcast that velocity is position final minus position initial. Over time final minus
08:24
time initial. And that’s all we’re doing in slope. In other words, the slope of this line
08:30
is giving me the velocity of that object. So to solve that in a more round about way,
08:37
let’s kind of go down to this next one. So let’s go right here. And figure out the velocity
08:43
of the man here. Well if we look down here, the final position is 3 meters. The initial
08:52
position is 6 meters. The final time is 8 seconds right here. And the initial time is
09:07
5 seconds. And so this should be negative 3 meters divided by 8 minus 5 is 3 seconds.
09:19
And so during this period of time the speed of the man or velocity is negative 1 meters
09:26
per second. And so our speed here was 2 meters per second. Our speed here is 0. Because the
09:34
man is not moving again. And then down here it’s negative 1 meter per second. And then
09:39
finally it’s 0 again. And so if we clear this off, again a goal was to be able to graph
09:45
that. So I’m going to graph this as, put this as 0 velocity right across the middle. And
09:51
so from position 1 to position 3, so position 1 to position 3, what was the velocity? The
09:58
velocity was, and let’s make this one and make that 2 on our scale. So from here to
10:04
3 the velocity was actually 2 meters per second. It’s going to be a straight line. Now what
10:11
was the velocity from this period? So from period 3 to period 5. So time 3 to time 5
10:17
was actually 0. So I’m going to draw a straight line right across here. And the you can connect
10:21
that with a vertical line like that. Should be straight vertical. Okay. So the velocity
10:27
was 2 meters. Then it was 0 meters per second. What has it during this period of time? We
10:31
just calculated it. For the next 3 seconds, 1, 2, 3 it was negative 1 meter per second.
10:38
So 1, 2, 3. It was negative 1. So we’ll call this negative 1 right here. And this would
10:45
be 1. And then what was it at the end? At the end it was 0 again. And so this would
10:51
be the velocity versus time graph for that object. It was going a constant speed in the
10:57
positive. In other words The Moving Man was moving to the right. He then paused for a
11:02
little bit of time. He then went in the opposite direction. Not as fast. You can see that the
11:08
slope of the line is not as steep as it was over here. And then the man waited for a period
11:13
of time. And so that’s how you would go from a position versus time graph to a velocity
11:22
versus time graph. And the easy way to do that position versus time to velocity versus
11:28
time is just to figure out the slope Because if you figure out the slope of the position
11:32
versus time graph that will always tell you the velocity versus time graph. If that doesn’t
11:39
make sense, go play. It’s phet.colorado.edu. Play with the Moving Man and then take a stab.
11:48
Now if you play around a little bit what you’re going to find is that it’s not always as straight.
11:53
In other words when we were doing it, moving man was moving straight to here. And then
11:57
resting. And straight to here and resting. But in this graph, you see that it’s actually
12:02
a curving line on the velocity. And what that means is, or on the position versus time.
12:07
And that means that its velocity is changing. So you could try to figure out what the velocity
12:12
versus time graph is. Or you could watch position versus time part 2 and I’ll give you some
12:18
tips. So I hope that’s helpful.
—
This post was previously published on YouTube.
—
Photo credit: Screenshot from video.