You know what? I am NO Theorist.
Instead, lets use a real-world example.
On my motorcycle, I have basically had in in three different configurations. No, wait, the damaged YellowTop would count as another. Four configurations then.
When I first rigged up my cycle, it ran on three small SLA batteries in series. So, that's 36 volts, but you can't pull very many amps from them. Speed was decent, acceleration was OK. Range was poor (low Amp-hour batteries)
When I switched to three Optima Yellow Top batteries, the speed really didn't change at all, but acceleration was greatly improved (these batteries can handle much higher current) and range was greatly improved as they were 55 AH batteries instead of 18 AH batteries.
Then, I added a fourth YellowTop. This increased my system voltage to 48 volts and increased my top speed from 35 mph to 45 mph (made it to ALMOST 55 down a big hill once...)
However the acceleration felt like it was still about the same.
Still, my top speed and range both increased - both of which tend to be important to motorcycles.
Now here's a weird one. Shortly after increasing to 48 volts, I damaged one of the YellowTop batteries. OK ok. I melted the post completely off.
I then tried repairing it myself, but the cycle never had the same acceleration after that. I think what happened was that my poor repair limited the amperage that could get fed through the battery.
Later, my home repair eventually failed. I removed the 4th battery, and was now running on only 36v. But guess what? The bike got its pep back! Suddenly, I had my zippy acceleration again.
Later, I found a battery place that repaired my post (free of charge! Great guys!
) So, now the cycle is running 48 volts, with good range, speed, and acceleration.
So, getting back to MazdaMatt's question, it's my opinion that Acceleration (is that the same as Force? or Torque?) is proportional to amperage.
Using 36 or 48 volts didn't seem to make a difference in acceleration, just speed. Using a different style of batteries, which couldn't pull as much current didn't change the system voltage, or speed, but did effect acceleration.
A damaged battery also didn't effect voltage, but seemed to limit amperage, and acceleration was poor at that time as well.
Now here again is something of interest.
Some batteries don't handle amperage as well as others. AGMs are very good, and a nice choice for motorcycles.
When you use higher voltage, you pull less amperage to do the same amount of work. At a certain point, amperage is limited by the characteristics of the batteries - their size, chemistry, state-of-charge, etc.
Running batteries in series can reduce the amperage needed and thus keep the amps below the "wall" of what the batteries can keep up with.
I think that on the motorcycle, the controller (300 amp 48V) is the limiting factor because I have some very nice batteries that can keep up with that.
On my Electro-Metro, I believe the batteries are the limiting factor. At the end of a drive, it's uphill and the highest speed limit of any where I drive. In third gear, I can have the pedal to the metal, and the ammeter won't budge past 250 amps. I can upshift to increase this, but then the battery voltage drops like crazy - ie. the batteries are NOT happy.
If I had 12 batteries in series, instead of 6, only half the amperage from each battery would be needed. I believe that this would then mean that I would have more amperage available from the batteries, and could accelerate a bit more to get to that higher top-end speed.
So, in summary. My real-world experiences do seem to indicate that amperage has pretty much everything to do with acceleration. Howerever, higher voltage has lots of other advantages, including keeping your batteries happy and higher speed.