Originally posted by dadudemon
Accelerating 1g for one hour.
That means it is accelerating 9.86m/s/s.
If we assume that it's relative motion is 0 at the start of this hour then that's as simple as multiplying the number of seconds out:
3600 seconds * 9.806 m/s/s = 35,301 m/s is the final velocity. To accelerate, negatively (as they say in physics...but we commonly call it "deceleration"
, it's as simple as it being -9.86m/s/s for one hour.
So there's the first portion.
*reads the rest of the post*
Edit -
Yes, there is a formula for figuring out the distance traveled through the acceleration vectors (both the positive and negative vectors WILL add to the total distance traveled, but, thankfully, once you figure out one, you just multiply that by 2 to figure out the other.)
So, first, figure out total distance traveled for just the acceleration vector.
Double edit -
So, if I remember the formula correctly (didn't have much googling), it's vt + (a*t^2)/2 = d
d = distance traveled
v = initial velocity.
Since the initial velocity is 0, we can throw that out.
Doing the math, that's 63,542,880 meters.
So that's how long it traveled during it's acceleration vector.
Double it because it wil be exactly the same through the negative acceleration vector.
So that's 63,542,880*2 = 127,085,760 m
So, now we are 2/3 the way done. We need to find out how far it traveled during that one week period.
triple edit -
K. did the math. It works out.
I converted one week to seconds, to keep like terms.
7 days = 168 hours
1 hour = 3600 seconds
3600*168 = 604800 seconds
It is traveling at 35,301 m/s for 604800 seconds.
Multiply that out:
That's 35,301 m/s * 604800 seconds = 21,350,044,800 meters
Now, add your acceleration vectors in:
21,350,044,800 m + 127,085,760 m = 21,477,130,560 meters traveled.
There's your answer.
Did show enough work for you or do you want me to be more thorough?
I edited the above post for the correct g.
g = 9.806
Yes, I eliminated some precision, unsoundly.