Everytime I start my car, RPMs jump between 1.5k and 2k and stays there for a good 5-6 seconds (engine seems to be accelerating) then it'll drop just below 1k RPM and the engine will smoothe out. Is this normal?

 

My 06 350 does this as well, I believe it is normal since its put to a higher rev so that it has oil flowing quickly to the engine parts and having it to be protected sooner while also increasing engine temps so that it warms up the oil to pump easily as well. Also when its a colder day outside say under 40f it revs up a few seconds longer so that the oil temp can maybe heat up quickly too since it may take longer for the oil to warmup.
i have a 5.9 diesel truck that does this too sometimes when its around 40f where it revs up to 1k and stays there for 30 seconds to 1 min to warm things up quicker and also pump oil quickly too, since most wear for an engine is on start up im sure the engineers did this to prevent that wear as much as possible.

 

On a cold start, yes, the slighter higher than normal rpms at initial start-up is normal.

 

Ok good! I was worried maybe I was having a transmission problem. And I meant everytime I first start my car, anytime after that shes nice and smoothe. Thanks fellas

 

Where I grew up -IF - it starts - ITS ALL GOOD!