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Mr. Andersen explains the basic quantities of motion. Demonstration videos and practice problems are also included. The difference between scalar and vector quantities is also discussed.
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Transcript Provided by YouTube:
00:05
Hi. This is Mr. Andersen and today I’m going to be talking about speed,
00:10
velocity and acceleration. If you’ve ever seen Usain Bolt run from Jamaica, well, first
00:15
of all it’s highly impressive. But you have an understanding of how fast fast really is.
00:22
In physics we deal with really just two of these. In other words speed is a scalar quantity.
00:32
And you’ve used speed you’re whole life. You say my car can go 20 miles per hour. Or my
00:36
car can go 200 miles per hour. And we’re talking about speed. It’s a scalar quantity and if
00:43
you don’t really know what a scalar quantity is, make sure you watch the video on that.
00:47
But velocity and acceleration are vector quantities. And so they include not only the magnitude
00:54
but also the direction at which a velocity or a position might be changing over time.
01:02
And so in this video I’m going to show you how to do some simple problems with velocity
01:06
and acceleration. Kind of explain what it is. But we’ll get into a lot more detail when
01:11
we look through position versus time and velocity versus time graphs eventually. So let’s get
01:16
going. Before I get started however, there is a little cheat that I want to remind you.
01:21
And that’s because I live in the US. And since I live in the US I really have a hard time,
01:26
dealing just in my brain, with meters per second. And so if you do any problem is physics
01:31
you always have to use the units meters per second. But in the back of my head I have
01:35
this. In other words if I say something is going 10 meters/ second, in the back of my
01:40
brain I have to think that’s about 22 miles per hour. Because that gives me an idea of
01:44
really how fast something is going. So if you want to use that in the back of your head
01:49
you can. But don’t use it in here, equations. Or you’re going to get the wrong answer. Now
01:53
velocity is a vector. And what does that mean? When you’re ever talking about velocity you
01:59
have to say, not only let’s say 2.6 meters per second, but you have to give me the direction
02:05
that that’s moving in. So it could be north. It could be west. Or it could be up. Or it
02:10
could be down. And so if you ever give a velocity make sure you have the direction. Now you’re
02:16
going to find immediately in this video that I quit talking about direction. And so you
02:21
may think he just told me direction is important but now he doesn’t even use direction. And
02:26
the reason why is that we generally use a coordinate system like this. And so if an
02:31
object is moving up, we’ll say, then it’s going to have a positive velocity. And so
02:37
that positive actually tells me that direction it’s moving in. Or if it’s not sitting on
02:41
something and gravity pulls it down, then it’s going to move in the negative direction.
02:46
Or in the problems today, Usain Bolt, I’m going to assume, is starting at the origin
02:51
and then he’s running in the positive direction. But if the wind came up, a real big wind and
02:56
blew him in the opposite direction then he’d be moving in the negative. And so I’m not
03:01
cheating. I’m actually including positive and negatives to explain that. Also you should
03:06
understand the different between and average and a instantaneous velocity. An average velocity
03:12
is looking at a certain period of time and saying how fast it had moved during that period
03:16
of time. But along that race of Usain Bolt, he has all these different instantaneous velocities
03:22
that are a little bit different. And the best way to explain that is with maybe with some
03:25
videos that I just shot. So let me bring up one of these. This is a video of me, let see,
03:32
go back to the beginning. So this is me taking a weight and then just dropping the weight,
03:39
like that. So what I can do, let me go back for just a second. If I go right here, and
03:44
I think I should be able to draw on this. So what I can do is I can actually mark where
03:50
that weight is. So let’s go back a second. So right here the bottom of the weight we’ll
03:54
say is right there. And now it drops the frame and the bottom of the weight is right there.
03:59
And it drops a frame and the bottom of the weight is right there. And now it’s right
04:04
there. And now it’s way down here. And so what we can look at is that this is an object
04:10
that is changing in velocity. And so it’s velocity way up here was actually zero. And
04:17
then it’s velocity changed and it got faster and faster in the negative direction over
04:22
time. And so that would be an instantaneous velocity wherever it is. But I could also
04:29
take this whole thing and figure out what’s the average velocity over that. And so make
04:35
sure you kind of understand the difference between the two. Let’s try another one of
04:40
these. Here’s another one, a video I just made. So this is just an object that’s rolling
04:46
across the table. So let’s get that back again. So I’m going to give it an initial push like
04:55
that. So I give it an initial push and then according to Newton’s Laws an object in motion
05:02
tends to stay in motion. And so I’m going to mark the middle of the object right here.
05:08
It’s going a little slower. So let’s go a couple, 1, 2, 3 frames. Now it’s right here.
05:11
1, 2, 3 frames and now it’s right here. 1, 2, 3. 1, 2, 3. 1, 2, 3. 1, 2, 3. 1, 2, 3.
05:27
1, 2, 3. 1, 2, 3. Okay. And so I gave that an initial velocity. And if you look at it,
05:37
it seems to be uniform. And so in this case, we’d actually have an instantaneous velocity
05:43
at any one point that’s actually equal to this average velocity over the whole distance.
05:50
And when we get to doing some graphing that will make a little bit more sense. But remember
05:57
there’s a difference between the two. And so I kind of will use them interchangeably.
06:00
But make sure you understand which of the ones I’m talking about. Okay. So definition
06:05
time. If you need to solve some problems, this is the definition for velocity. So definition
06:10
of velocity is simply change in x over the change in t. Where x is its position and t
06:17
is equal to the time. And so to solve a problem that you might have like on a worksheet or
06:22
a test, let’s do Usain Bolt. So his world record in the 100. meter dash in 9.58 seconds.
06:31
And so to figure out his velocity, this is how it works in my brain, I go delta x over
06:35
delta t. So delta x is simply the change in x over the change in t. And so how far does
06:41
his distance change? Well it’s going to be 100. meters. Always make sure you’re including
06:48
the correct number of significant digits and the units as well. Otherwise you’re going
06:51
to get stupid answers. Now we look at the change in time. Well the change in time is
06:56
9.58 seconds. Okay. So how do we do this? We’re going to divide 100. meters divided
07:04
by 9.58 seconds. I did that just a second ago. And I got 10.4 and units then are going
07:13
to be in meters per second. And so the average velocity of Usain Bolt during his whole run
07:18
is 10.4 meters per second. Using that brain trick again, if I take that times 2.2, he’s
07:23
going roughly 23 miles per hour. To give you an idea of what his average speed is. And
07:30
so that would be a pretty simple velocity kind of problem. Sometimes it doesn’t start
07:36
from rest. In other words it doesn’t start from a time being 0 and a velocity being 0
07:43
as well. And so a better way to remember what velocity is instead of the change in x over
07:47
the change in t is it’s the final x or it’s final position minus it’s initial. And so
07:53
get used to this in science. The f always stands for final. And the i always stands
07:57
for initial. Divided by the final time minus the initial time. And so this is a better
08:03
way to explain what velocity is. And let’s try a problem where it actually varies a little
08:08
bit. These are the splits from Usain Bolt’s race. This is actually in the Olympic record
08:15
where he ran an 9.69. And so the first thing let’s do is let’s try to figure out the velocity
08:21
for the first meters, the first 10 meters. And so velocity remember is going to be xf
08:28
– xi where xf is the final position. And then it’s going to be tf – ti. Okay. And when you
08:39
ever solve problems you want to make sure you identify what do I know. Well what’s the
08:42
final position? That’s going to be 10.0. So 10.0. What was his initial position? And again
08:50
I should put meters. What was his initial position? That was 0. So that’s minus 0. What
08:57
was his final time? That would be 1.85. \b
09:03
\b0 And then what was the initial in seconds? It’s 0 seconds. So what I get here is well
09:12
roughly 10.0 meters over 1.85 seconds. And so when I worked this earlier, I get 5.41.
09:20
So it would be 5.41 m/s. Now why does this have 3 significant digits? Because that has
09:31
3 and that has 3 as well. So how fast is that in miles per hour? It’s not very fast, 13,
09:39
14 miles per hour. Let’s look how fast he’s running later in the race though. Let’s try
09:45
it way down here. If we go way down here. Let’s say at this point. So remember velocity
09:52
is going to be final X minus initial X over time final minus time initial. And this is
10:02
why, you’ll start to see why it’s important that we kind of keep track of that. During
10:09
this next 10 meters he ends up at 70.0 meters. And he started and 60.0 meters. So this would
10:21
be the initial distance. The final time is 7.14 seconds. And the initial time is 6.32
10:33
seconds. And so what does that equal? Well that equals 10.0 meters divided by .82 seconds.
10:45
And so the right answer should be 12.2 m/s. So that would be the right answer. With three
10:53
significant digits. Doing that into miles per hour, it’s around 27 miles per hour. So
10:58
it’s a ridiculous amount of speed. And so this would be his speed down here. 12.2 meters
11:05
per second. And remember when we were way up here his speed was only 5.4 meters per
11:12
second. And so what has happened from here to here? Well the velocity is actually increased.
11:21
And so you know what that means. What does it mean when you’re velocity is increasing?
11:24
That means that we’re accelerating. And so not only is the velocity important but what
11:29
happens to the velocity over time is also important. And so that’s what acceleration
11:33
is. Acceleration is the change in velocity over the change in time. And if you look,
11:39
the equation is very similar. We take the final velocity minus the initial. And then
11:44
divide that by the final time minus the initial time. Now the units are a little bit weird
11:48
if you think about it. We’re taking meters per second, which is what the velocity is
11:53
measured in. And we’re dividing it by a second. And so lots of times we’ll just write that
11:58
as meters per second squared. Now what’s one acceleration that you should learn. This is
12:03
the acceleration due to gravity. So the acceleration due to gravity is -9.8 meters per second squared.
12:09
What does that mean? If we take a person like this, standing at the top of a cliff. And
12:15
they fall off. At 0.0 seconds they’re going to be going 9.8 meters per second. Excuse
12:22
me. At the top they’re going to be going 0.0 meters per second. But after 1 second they’re
12:28
going to be going 9.8 meters per second. So if you jump off a cliff. After one second
12:33
you’re roughly going 23 miles per hour. After two seconds you’re going 46 miles per hour.
12:40
After 3 seconds you’re going, you know, 68, whatever, miles per hour. And so you’re going
12:44
to go really really fast very quickly. And so that’s acceleration due to gravity. Why
12:48
it’s in the negative is that remember on our quadrant system this would be in the positive
12:53
and so this would be in the negative as we go down. Let’s try an actual problem. How
12:59
you would have to solve a problem like this. This is the Bugatti Veyron, which is made
13:03
by Volkswagen. And it’s the fastest production car that you could buy, if you have a bunch
13:09
of money. Goes like 250 miles per hour. And so let’s try to do an acceleration problem.
13:15
So acceleration remember is the change in velocity over the change in time. So let’s
13:21
figure out if it can go from 0 to 60 in 2.46 seconds, what kind of acceleration are we
13:27
talking about. So again, that’s going to be vf – vi over tf – ti. So what’s our final
13:37
velocity? Our final velocity is going to be 60 miles per hour, which we couldn’t use in
13:43
an equation. We have to convert that to meters per second. So that would be 26.9 meters per
13:49
second minus 0. Because it starts at a stand still. What is it’s final time? It’s final
13:56
time is going to be 2.46 seconds minus 0 seconds because it goes from a standstill. And so
14:03
now we could figure out the acceleration. So 26.9 divided by 2.46 is going to be 10.9
14:11
meters per second squared. So that would be the right answer. So going back again and
14:17
figuring out what the acceleration due to gravity is, if you’re falling off a cliff,
14:20
you’re going to experience an acceleration in the negative or down of 9.8 meters per
14:24
second. If you’re sitting in this car you’re actually going to feel more acceleration than
14:30
you would falling off a cliff as you acceleration. And so I don’t know what that’s like, but
14:34
I bet it feels really, really cool. And so I hope that’s helpful.
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This post was previously published on YouTube.
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Photo credit: Screenshot from video.