I have a 2006 Hyundai Matrix 1.6 GSI petrol. Automatic. When cruising at 4o mph it starts jerking and seems like it has a problem selecting the right gear. Also at around 60 mph it jerks when I accelerate.

https://www.youtube.com/watch?v=lJUOOrQqKJI

EVAP system problem

Check this link for timing chain images:

2006 Hyundai Matrix 1 6 Timing chain Google Search

this will help with the video:

How to do Hyundai timing belt

check your battery voltage a weak battery can minic a faulty fuel pump. your voltage should be 11.6- 14 volts

Have you had the car tested for fault codes? Do that first.

make a mixture 1 liter two table spoon of salt in bottle with spray
engine idle spray your mixture not too much and see if you have spark on wire ,coil you won't see it if too much mixture
and about spark plugs you could change it too
you have a misfire

fuel pressure cud be bad at that speed--transmission may hav issue in top gear--find a specialist to test--------

I just bought a 2011 Sonata and am experiencing the same problem. Going downhill with cruise set at 55 mph; speed increased to 70 mph and was still accelerating (from the downhilll grade) when I finally pressed on the brake.
This is not normal. My Honda Accord never varied from the cruise setting by more than 3 or 4 mph ... going uphill or downhill.

You have to have the DTC pulled to see what made the light come on , ECU is a common problem on this vehicle,it is covered for 8 years/80,000 miles

I had something similar happen. My check engine light never came on but i did experience the jerking between the 30 and 40 mph mark. Have your fuel injector checked to see if its dirty. Also have your fuel lines checked to see if you have water in it and have them check the transmission fluid. its possible you can be low. When I had the problem i did all 3 of these things. My car does not **** anymore. Also another problem could be your valve cover gasket.