It could be tires or brakes
Hard to tell from my computer keyboard
And from what little information there given

 

ok I'll have tires and brakes checked

 

I have the same problem on my 2005 Santa Fe. Thought it might be bad ball joint or tie rod, ...but no. It seems that right after I had an alignment, I started to experience the problem. I think that the mechanic who did the alignment had to "muscle" the tie rod nut so much that he messed up the front rubber bushing on the control arm. Jack up one side at a time with the tires on, grab the tire at the 9 and 3 o'clock position and wiggle it inside and out while looking at your control arm. If the control arm moves at all horizontally that may be the source of your problem.

 

Keeping in mind that when accelerating the engine mounts have to move one way and when decelerating the mounts go in the other direction. With front wheel drive the transaxle is mounted to the engine and torque is applied and released to the front wheels. The object is to determine why the wheels are moving out from the straight ahead position when for example torque is applied. Good possibility something is either loose or worn. Sometimes this can be seen when power braking the vehicle with the brakes applied in forward and reverse.

 

 

 

 

Check for open recalls on your vehicle
Hopefully there is one on lower control arm or subframe

Good luck

 

I think I would put my own eyes on it or maybe get a second opinion. make them show you where the bad parts are on the control arm.