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