In article ,
JJ wrote:

I was watching a NOVA program on how some astronomers came ot the
conclusion that the universe was expanding, something I thought was
always known.

Nothing was "always known". Most facts about the universe
was obtained through a series of heroic struggles which began
with the formation of life billions of years ago. Every bit
of knowledge is precious.

In the vacuum of space, there is more than just a vacuum. There are
millions of little particles, constantly popping in and out of
existence, if i'm not mistaken.

This is a sort of metaphorical picture of quantum field theory,
which has to be taken with a grain of salt. Unfortunately this
grain of salt can only be obtained in a course on quantum field
theory.

Now if the universe is constantly
expanding then everything in the universe is moving, not just moving,
accelerating. Now, while we are hurtling through space, we must be
hitting those particles in the vacuum. So eventually, trillions of
years later, won't the amount of resistance from hitting those
particles built and we'll slowly come to a steady speed?

No. We aren't really hurtling through anything. To understand
this you first need to understand how distances between galaxies
can increase even though each galaxy is almost at rest with respect to
the only sensible notion of "rest" - the cosmic microwave background
radiation. You then need to understand how there's no difference
between sitting still in a sea of virtual particles and zipping
through it at high speed. Both these facts are the sort of thing
covered by "relativity theory". They take quite a while to understand!