Hello, and welcome.
This will be the first in the series of lectures on physics.
My goal is really to give you an intuitive feeling of what
physics is all about, because especially on the mechanics
side of things-- projectile motion, force, and momentum--
it's actually pretty intuitive.
Let me know if I'm not giving you an intuitive sense.
Let's just start with probably the most basic formula in
physics, and a lot of you have already seen this: it's
distance is equal to velocity times time.
You might have seen it in different forms-- you might
have seen it written as the distance is equal to rate
times time, distance is equal to speed times time, or
instead of a d, if you're doing it in math class,
sometimes you'll write an s for distance, because they use
d for derivatives-- but it's all the same thing.
It just says the distance you travel is equal to the speed
or the velocity you travel times time.
Before I do a couple of quick example problems just to hit
this point home, I just want to make a slight distinction
between velocity and speed.
When people use it in everyday language, it tends to be used
interchangeably-- it's how fast are you going, velocity
versus speed.
Technically, there's a difference: velocity is a
vector of measurement, and speed is a scalar.
I probably have already confused you, but all you have
to know is a vector has a magnitude and a direction.
If I were to give a velocity, I really shouldn't just say
five miles per hour.
I should say five miles per hour north.
Or, instead of saying five miles per hour north, I could
say negative five miles per hour south.
Right?
Those would be the same thing.
Speed, or a scalar, only has magnitude, so speed would say
five miles per hour, but I don't know what
direction I'm going in.
I could be going forward, backward, left, right, north,
south, up, down, who knows?
That's the technical difference between a vector
and a scalar and between velocity and speed.
It might not seem so obvious, and probably on these few
example problems we're doing right now, the distinction
probably could be used interchangeably.
Later on, as we progress to fancier problems, I think
you'll see that velocity is a more useful notion, because
there's the idea of a negative velocity.
You can go in one direction, which is positive, and then
you can turn around and go negative.
With speed, there's no direction involved.
With that said-- I don't want to dwell on that too much,
because I don't want to make you think that this is
difficult-- let's do a couple of really quick problems.
Let's say I went 50 meters, so distance is equal to 50
meters-- I go 50 meters.
Time is equal to-- this is should really be distance,
because it actually changes in distance, but for the problems
we'll do, it doesn't make a difference-- let's say the
time is-- and this could be change in time, as well, the
time is 10 seconds.
So if we use that formula, we have 50 meters is equal to
velocity times 10 seconds.
This is a pretty simple algebra equation.
If we want to solve for velocity, we just divide both
sides of this situation by 10 seconds.
I'm doing this because I actually want to show you that
when you divide the numbers, you should also divide the
units with them, and then you always end up
with the right units.
Let's multiply both sides of this equation
by 1 over 10 seconds.
I get 1 over 10 seconds times 50 meters is equal to velocity
times-- I'll write it all out, later on, I'll skip some
steps, and this obviously cancels out, because that's
why we did in the first place-- and then the 50 and
the 10 cancel and this becomes 5.
We're left with 5, meter in the numerator, and the seconds
in the denominator.
I could write it as sec, or just an s-- so 5 meters per
second is our velocity, and you could have done that.
The one thing I just wanted to highlight is that the units,
you can manipulate with the numbers, and then you always
get the right answer.
It might have been obvious in this case-- you didn't have to
do it this way-- but once again, later on, when we start
doing power and work and energy, which is actually the
same thing as work, but once we start doing those things,
then the units might not seem so obvious.
It's good to be able to deal with the units this way.
We could solve-- if I said that the velocity is equal to
7 meters per second, and that time is equal to 5 seconds--
how far did I go?
I could use that formula again: distance is equal to
velocity, which is 7 meters per second, times time, which
is 5 seconds.
Once again, not only can we multiply the numbers-- 7 times
5 is 35-- but we can multiply the units, so we have meters
over second times second.
You can almost treat them like variables, but they're not--
they're units.
Meters over seconds times seconds-- the second in the
numerator and the second in the denominator cancel out,
and so you're left with 35 meters.
There-- not only do you have the right number, you have the
right units.
Actually, this is going to be super useful when you have to
convert from centimeters to meters, and hours to seconds,
and all of that-- maybe we'll do a couple of examples.
Actually, a while ago, I actually made a separate video
on unit conversion, and that's going to come and really handy
when we do the physics.
With that out of the way, let's make things a little bit
more complicated.
Most of what you've probably experienced so far-- distance
is equal to velocity times time, or rate times time-- is
where velocity is constant.
You're going 30 meters per second, you're always going
the 30 meters per second, and you'll stay going 30 meters
per second.
But we know from moving, generally, that your velocity
isn't-- sometimes, you're stationary, then sometimes
you're moving, and in order to start stationary, and then get
moving, your velocity has to change.
How could we describe a change in velocity?
Once again, I don't think I'm teaching you anything
fundamentally new.
You know what it is-- it's acceleration.
So, velocity is acceleration times time.
There's a pretty good analogy here: just as distance is
velocity times time, and velocity is
acceleration times time.
Or, you view it as the change in distance over the change in
time is velocity, while the change in velocity versus the
change in time is equal to acceleration.
My phone's ringing-- let me answer that a little bit
later, because once again, you are more important.
So where was I?
I was saying how they're very similar-- at least, there's
kind of an analogy here.
What can we do with this notion?
I'm going to do a bunch of what I think you'll find is
pretty useful-- they're called projectile problems, and
projectile problems involve the acceleration of gravity.
We could do other acceleration problems involving the
acceleration of cars, and actually, I
probably will do that.
The acceleration of gravity is actually 9.8 meters per second
downwards-- once again, acceleration is actually not
downwards, but towards the center of the earth.
Acceleration is also a vector quantity, but for the sake of
our computations, we'll just say 10 meters per second.
Acceleration is equal to g-- g is normally the variable used
when people talk about the acceleration of gravity, and
let's say that equals 10 meters per second squared.
I know what you're thinking, that this is kind of a strange
set of units-- meters per second squared, and it's hard
to visualize.
That's acceleration, and I think once you see it used in
some of these formulas, it'll start to make a little sense
in terms of how these units work out.
Let's start with a fairly simple problem.
Let's say I drop a rock from-- I don't recommend you do this,
you could kill somebody-- not a rock, a penny, from the
Empire State Building, and I'm assuming no air resistance.
Actually, I just looked at the clock, and I realize that I'm
running out of time.
I'm going to actually start this problem in the next
presentation.
I'll see you soon.