Someone else has suggested the spark plugs would this cause the stuttering under acceleration ?
A car only needs 3 things to work.
Correct quantity of air.
Correct quantity of fuel.
Spark at the right time.
If one of these is missing, you'll get poor combustion.
It's also easier to start closest to the cylinder and then work backwards.
Even if the spark plug isn't the problem, it will give an indication to the problem by what it looks like.