I'm sure that there are many correct answers to this question.
Sputtering usually happens when there is a lack of fuel or spark when the engine attempts combustion.
Many things can cause an engine to sputter, however "sputtering during acceleration only" is often due to a lack of or an incorrect timing of spark. I suggest you have your spark plugs or coil pack checked. I'd guess that there's a better than 50% chance of that being the problem. If that isn't it, my #2 choice would be that you need a new fuel filter because when you accelerate the engine is trying to draw extra fuel and the fuel filter is limiting the flow of gas.
You will likely only be able to know for certain by taking it to a mechanic. I hope it's only the fuel filter. They are very inexpensive compared to a whole set of spark plugs or worse, a whole coil pack.
If it only happens when you accelerate the most likely cause is an axle.
I expect the motor to sputter to life any second, now... The clerk was so exasperated, he could only sputter.
Maybe low coolant level
your wheels have a censor built on the wheel bearing. the sensor could be going bad or the wheel bearing is also. if the abs light on is a sign of a wheel bearing.
An object will accelerate if and only if there is a net force acting on the object.
It sounds like fuel starved. Try the fuel filter or the fuel pump.
Often a faucet will sputter if there is air in the lines. This happens if the water has been turned off and then on again. If this is the cause, it is only necessary to run the water a while and the air will get out of the lines, and the sputtering will stop.
You need to use premium fuel, the fuel u are using can cause predetonation, and cause knock. Which will ruin your engine
Objects in freefall only accelerate at 9.8m/s2 if air resistance is ignored. Because friction will gradually cause a falling object to reach terminal velocity, most objects won't accelerate at exactly 9.8m/s2.
Fault in the Crankshaft position sensor
if it tends to sputter and have no power i would suggest the fuel pump. it it is only after the car has warmed up, or a while after you start driving it might be the ignition module.
According to Newton's laws, the conditions in which a body accelerates are only those in which a force is acting upon it. With no force acting upon it, a body would not accelerate. With a force acting upon it, it would accelerate by an amount proportional to the force and inversely proportional to its mass.