and can i put a turbo on a honda accord 03 V6 automatic transmission?

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Absolutely…
However, despite the quality of Honda engines, their trannies are some of the weakest & aren’t known to last as long as other auto makers.
Adding boost to a car w/an automatic really is a waste of time & money. The main reason is because it’s an automatic. You can’t really take full advantage & get the full effect of using boost on your engine. Also, since it’s already an automatic & once you add a turbo, you can further kiss your gas milage good-bye lol.
You are better off either converting your Sol to a stick by doing an engine swap (that takes some work there, too) & adding boost then. However, again, it’s another factor of time & money. If you are really planning on doing some major work to this car to make it show quality & really make it into something worth the bragging rights, then ya, doing a swap & conversion, then adding boost would totally be worth it. Otherwise, sadly, as much as you probably love your Sol (& trust me, I feel the love lol), you just won’t get back what you put into it, unless you plan on making it a show car.

so i was driving for about an hour and a half or so around my city (some hard acceleration) and near the end of my trip my 300zx started to run really rough it was making this putting noise and i say that because it sounded like a Harley “put put put put” and during acceleration the putting became quicker i could even smell a very slight burning smell i got to my house and let my car cool down as soon as i got home i lifted the hood but no burning smell i assume the smell was coming form the exhaust. anyways the next day i started the car and it ran fine then after about 2 minutes of driving the problem started again with the putting but no smell this time i was driving close so i continued driving and i saw my radiator light flash on for a minute then turned off. also the rpm is bouncing wit the putting noise and is up and down really fast. and also this is only in drive not in park as soon as i put it into drive the rpm drops to maybe about 500prm and bumps up and down… and again whel i rev it its a harsh putting rev.

if yes, would it increase its power or is not worth it to buy a turbo kit.