So I am having trouble with a problem.. and this has been a thorn in my side for quite some time now. I am working on a science fiction idea where I use the rate of expansion of the universe as the rate of acceleration of a spaceship. The rate of expansion is about 70 km/sec/megaparsec.. and I think the megaparsec is throwing me off because when I reduce it to just km/sec, it's an incredibly small decimal with something like 18 zeros. Plus, for some reason.. acceleration seems to be kicking my butt. So I was wondering if I could use a shortcut of sorts. If I knew the amount of time it'd take if I traveled at the initial velocity and knew the amount of time it would take with the final velocity, can I just take the average of those 2 times? For example, if I wanted to travel 7 billion light years and my initial velocity was 1/2 the speed of light.. if I traveled at 1/2 light speed the entire trip, it would take me 14 billion years. My final velocity is the speed of light, which if I traveled at light speed the entire trip.. it would take me 7 billion years. The average of those 2 times would be 10.5 billion years.. so my question is this, is that right? If I were to travel 7 billion light years and had an initial velocity of 1/2 the speed of light and my final velocity upon arriving was the speed of light, would it take me 10.5 billion years? Thank you in advance.