I would say you either have a rod knocking or lifter knocking. I know in the 3.8 litre motors they are known to knock alittle when you cold start them. Most Grand Ams, Grand Prixs are like this. My sister has a 2002 Grand Am that does this and the noise goes away once it's warmed up. I would also double check and make sure your oil is full. get your car to a garage for a def solution.
The knocking noise is commonly called spark knock. The knock can be called by the engine timing not being set correctly, or using gas that has too low of an octane for the engine.
A knocking noise can occur from worn engine mounts. When the rubber insert on the engine mounts are old and brittle the chassis is not protected from the weight of the engine. Creating loud vibrations that get louder as the vehicle goes faster.
When you accelerate. you are putting presure on the main engine barrens. if they are going bad. You will hear this knocking sound. I don't know how many miles you have on this engine. But that's what it sounds like. But that's not all that can make this sound. You will have to tell more about it and when it started. Did it just start all at once? or did it start and then get louder?
Most likely needs a tuneup done. Check the timing and change the normal tuneup part.
knock sensor is going bad or is bad
check cat converter if it has 75000 miles or more
If it's knocking when accelerating, the engine could be starving for the correct octane fuel ... try the mid-grade or premium fuel and see if it still occurs. Could also be that the timing belt needs to be adjusted/replaced. If the knocking sounds like metal on metal, chances are you are in for a bigger bill for a possible engine rebuild. At any rate, have it checked out by a mechanic soon.
My 99 sonoma had a knock and it was a wrist pin in the engine, my 99 jimmy fuel injection leaked gas in the engine oil and caused the main bearings to fail because of lack of proper lubrication.
knocking noise
when we accelerate vehicle the supply of fuel gets increased .. Then inside the combustion chamber all the charge can't burn in such case so phenomena of knocking takes place.. So the sound can be heared.
when kick down the gas pedal to accelerate, the car downshift but then stalls and then engine stays rough until i turn off the engine and restart it then the engine runs normal again till the next kick down.
a "knocking" noise could be your lifters. and the ticking when accelerating and letting out of the gas is the same thing. check your oil and if it's full then you may need to think about either having them adjusted, or getting new ones. depending on what you have depends on whether or not you wanna sell it