Dorkus Problem

OK, so I have big dorkwad issues. And they aren't met by my math abilities.

The Firefly - class ship Serenity is purported to:

can achieve an acceleration of 4.2 g, and has a maximum range of 440 astronomical units when carrying minimal cargo.^[9]

OK, that being the case, I've figured that "g" is about 9.8m/s/s.  4.2 g's (9.8 times 4.2) would then be about 41.2m/s/s.

My sister's dog Chien. AKA "minimal cargo".

If the Serenity can start instantaneously at 4.2 g's, how long does it take to get 440 astronomical units (one AU is 149,597,870.7 kilometers therefore 440 AU's is 65,818,663,108 kilometers)?

I am afeared calculus is needed to comprehend this. I mean, I could add up each second's speed (the first second we're going at 41.2m/s, second is 82.4m/s, etc.) But I don't really know how to do this as one formula.

• At 4.2 g's, how long does it take to travel 440 astronomical units? 

And to make life more exciting, what if you have to do your acceleration and deceleration at the same 4.2 g's? So does that mean that if you're going 440 AU's, 220 of them will be accelerating and the remainder 220 are decelerating?

Virginia Logan as Foxwell in Robowar.

• Math is hard. Does anybody understand this?
• Does it require calculus?