The higher velocity of distant objects is not related in the standard cosmoligical models to acceleration, but rather to the Hubble expansion law of the universe.

the hubble expansion law states that the velocity of an object expanding with the universe (i.e. no peculiar speed) usually called a comoving observer, from any other commoving observer is lieary proportional to the comoving distance between the two.
V = H*r ; with H standing for the Hubble constant at said time, H = H(t).

hubble law has been observationaly verified to a good extent (in astrophysics an order of magnitude is usually acceptable), and is also a direct result of assuming a non-static homogenous (and thus isotropic) univerese.

the hubble constant changes with time, or so the standard cosmological models say, and different models predict a different behaviour of H(t).
these are tightly connected to specific solution of the einstine equation, and to the metrics the solution enables (a homogenous universer results in one of three metrics- flat, positivly eccentric, and negativly accentric).

according to the standrd model today, the "lamda-CDM" model, which consists of a cold dark matter big-bang universe with a cosmological constant, the univeres' expansion rate should actually be increasing, thus u can say that the univerese is accelerating.
as far as i know it's not iron cast yet.
i can check with an astronomer in the huji astro-group for more detail on said observations.

Sorry if I'm being thick, (and you can write in Hebrew, if you wish, I'm writing in English only due to technical constraints) but how could they measure consequences of the Hubble law, if all one can do is check how galaxies behaved in the past, when it's not even the same time for all the other galaxies, since they're at different distances?

By the way: the Hubble constant changes with time? That reminds me of someone asking me about using different coefficients for his polynomial at different points.

English is preferable, i might be making some spelling mistakes, and i apologize for them, but the technical terms are all english, i hate to try and find translations...

first about the hubble "constant" changing -
the constant is constant in space, but not in time.
now, i'm about to step into a subject i'm no expert about, i apologize for any mistakes i might make -
the way to build a metric one can work with to describe the universe, in a GR way, is to "slice" it to equal-time three dimensional "planes".
the simplest way is to assume that the universe is euclidean at short ranges (observations of near space confirm that, near meaning as far as we can see, if i'm not mistaken), and then define a metric from a point of view of a "all-knowing" observer, that is one that can measure distances on the plane, between any two points.
now, for every two points on said metric, in every plane, the same hubble law holds, that is - the velocity between the two is proportional to a constant that is the same one in all space at that time.
the relation between said constant and the expansion rate of the universe is H(t) = a*/a (with a* being the time derivative of a, a "dot") where a is the expansion factor of the universe (has to be normalized to some a_0 if u want it to mean anything).

as for measuring galaxies at different times, i think that compensation can be done.
one way is to measure "near" galaxies, where time differences are small in cosmological orders of magnitude.
another, i believe, is measuring relative velocities of objects about on a line of sight (seems tricky to me, i don't know if it's actually done).
this is an interesting point, i think i've heard an answer to it once, and am sure i've asked it once, which make my not knowing it now somewhat dissapointing (and depressing, considering the implication about my memory), so i will check with my sources for the answer, and be back.

an important point, i think, is that predicitons can be made, according to the standard model, regarding what the hubble expansion should look like, if the modle's assumptions and derivations are correct, including "looking into the past" effects, and as far as i know the observations match those to a good degree.

be back with more precise answers soon, i hope