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