A = F/M (old physics formula) Acceleration =( Force/Mass) X efficiency
So what are the units" Well acceleration is a change in speed over time. It states that in the first unit if time (sec) it changes from 0 to the stated speed. After the first second it accelerates from the speed it is then to that much again and so forth. If you define a speed you want to hit you simply calculate how long that will take at the given acceleration rate. You can also express the numbers in "g's" or mili- g's . You can talk about acceleration on earth without using the magic number for acceleration of gravity of 32 Ft/sec^2 If you are sitting on a horizontal surface and the 'Mass" (weight of the gantry on earth) is not moving you have to apply a FORCE in order to accelerate it to a given vorticity at a set time period.
So far its just numbers. it simply says that for a given weight of gantry it takes a certain amount of force created from the torque of the motors and applied to the load though a transmission. Imagine two cars sitting at a stop light and both have 100 hp motors the same transmissions and both are in first gear. If one is a ponderous 3 ton 1973 Cadillac El Dorado and the other is a 1500 lb dune buggy which will reach 50 ft first? Which one can make a sharp turn and accelerate out of it quicker? Now put a 600 hp turbo charged engine in the Cadillac and do the same test.
So to sling a gantry around at high speeds you need a motor big enough keep the acceleration high enough. The heavier the gantry the bigger the motors you would need to hit the target acceleration. So the target of 35 iPS/sec says you can go from 0 to 35 ips in one sec. 35 IPS is 2100 IPM.
If you target speed is only 300 IPM than you hit that in .142 seconds . So how far have you traveled in .142 seconds ? The math gets a little hinkey because its during a move from 0 to 300 . but at 150 IPM as an average you cover about .355 inces
Acceleration is most important when you are changing directions (in any axis). An Arc is a change in directions in both axis. So why not just slow it down from 300 to 100 and give it more time to make the moves? Well you can but in plasma it changes how the arc cuts. The kerf gets wider , the voltage starts to climb and you start to see more slag. If you have a THC it reads the voltage for the height and it plunges the torch to try and "fix" the higher voltage. As you get below 20 IPS/sec acceleration it gets noticeable. At 10 ips/sec it makes cutting over about 80 to 100 IPM and doing tight turns or small arc or circles an ugly process.
One of the stats that a table provider should offer is the max acceleration. It should also list the max CUTTING SPEEDS (not rapids) and that should include stats to profile that with the fastest speed you can cut at with the THC tracking a 25% rise/fall from horizontal. 25% is a 1" rise in 4" inches or run. Unless the acceleration is high enough you may be able to cut at 300 ipm but you won't be able to turn a corner .
SO if you have plodded through this if you can come away with acceleration is tied to velocity and time and is defined by the amount of Force you have and the amount of weight you have to accelerate. I also hope you realize that the number you are looking for has been determined using trial and error over years. So to predict the max acceleration you can expect you have to have the Force ,which is how hard final drive can push on the load and is a function of everything from the moro torque , the motor torque at the RPM you need to get to the speed you want . the transmission ratios. Then you have to know the total weight and covert that to mass units by dividing by 32. The final piece of the equation is the efficiency which typically is about 25 to 30 %