Hello Rohela, welcome to our forums.
2008? You must have one of the last, newest S Types. Can you tell us more about it?
In the meantime it can be your fuel injectors may be dirty.
Put in some injector cleaner like RedEx or BG44K at Double strength to each full tank of fuel and do that for 2 tankfuls.
That will clean them for sure. I've used Wynne's recently but it didn't clean mine. So I'm trying to find RedEx or BG44K again.
Our member Bluechem's Oxicat is good for cleaning from the combustion chamber and out, but he (Richard) has another product for injectors and fuel path. Hope he spots this to advise.
Be sure you don't use the diesel engine version! I'm not sure why there are 2 types.
As 04str says, check fuel trims.
You can do that with an ELM327 (£10 on eBay in the UK) and your smart phone with the Torque Lite app or similar.
Or if you can go to £100 there is another far better code read/reset/diagnose tool others can tell you about (I'll leave something for them to tell you
It could be tyres? Cheap ones or worn ones can skip, there's a lot of power put down by these cars.
Listen for any clunking or banging under, the prop shaft has 2 rubber "doughnut" shock absorbers front and back which can split, and a centre bearing which can wear.
Lift the car up on a lift with the wheels off and check for worn bushes, balljoints, broken springs etc on the suspension.
The subframe mounts rot, check those too.
And the sills rot under the plastic over-covers, you'll need to get a pack of new clip screws for the covers, then remove them to check and put them back.
Hopefully yours won't suffer from these rots but it's best to check now.