Is the acceleration of the universe's expansion, constant or accelerating?

From the measurements made recently suggests the Universe expansion is accelerating. The prediction is the expansion will be so great that all matter will ripped down to individual atoms.... this is known as the Big Rip

"The only constant is the varying rate of change"

I don't think we yet know if the acceleration is changing.  And, the acceleration of the universe's expansion is a hypothesis that appears to be supported by observations, but is not sure or certain.  It has led to the postulation of dark matter and dark energy, but we don't have data about them yet either.

Here's a book that may help:
The View from the Center of the Universe   It's low math (almost none, actually).
The same authors have another book that extends their discussion.  Check your library, perhaps.

It's accelerating. When acceleration is constant it is no longer acceleration. It's velocity.

The basic equation calculus 1 and physics 101 starts with is y = x + v + a + c
where y and x = coordinates in a 2 dimensional Cartesian coordinate grid.
v = velocity
a = acceleration
c = constant = 0

First derivative = dx/dy = v + a  = c
Second derivative = d62x/ dy^2 = a +c
Third derivative = c = 0

The expansion *rate* is increasing, i.e., the velocity is increasing.

The big question right now is will this rate continue? If so, many astronomers are speculating that the universe will literally rip itself apart...whatever that means.

It is "accelerating" meaning, it is expanding and speed of expansion is increasing.

its speeding up it will eventually stop and the galaxies will be so far away from each other

THE RATE OF EXPANSION OF THE UNIVERSE IS ACCELERATING.

As simple as that, no craps =)

Hope it helps.