As title really.

My car is jerking if I accelerate slowly. It occurs both from standing and rolling starts and seems to happen at just above 20mph and just below 40mph.

It feels like a conventional auto that isn't changing smoothly.

The problem doesnt occur if more throttle is applied and seems to work perfectly in all other situations.

According to the service history I got with the car the oil was done at 80,000 and the car is now on 113,000 so is due a change soon.

Is an oil change likely to solve this or could it be clutch related or something even more serious.

I've read threads regarding CVT failures (and wish I had done so before buying the car) but I dont get any flashing lights or limp mode.