Silverblack correct...it takes a long time to go around the car with the DA polisher...if my car is clean, I generally apply wax by hand, it's a lot faster. I use the mequiars when the cars been slightly scratched, or last time, when dealership gave it a clean and it came back covered in swirl micro scratches...then you go through the stages...compound, polish...waxing, I just use the autoglym stuff I got with a car, and sometimes the liquid wax, but as said, do that by hand.
As said, I only said dewalt as already have 3 power tools etc so I would need body only....i'm not recommending it
Have no idea how long it would last, but I used to own a car jumper kit which had 3 pin socket on it...seen you can get them £45-£60...don't have mine anymore but they contain a car battery which you just keep on a charge at home..that might be enough to run a polisher for a bit, then you can choose any polisher etc..maybe worth giving halfords a ring..'some' of them know what they're talking about..then you could try a cheap £35 orbital polisher(as long as you keep moving it to do the daul action part) and see if it's good enough for your needs