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Old 2009-03-31, 12:04   #4
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17×251 Posts

Originally Posted by Andi47 View Post
Yes, we assume Newtonian mechanics, but you are far off.
Are you sure? I get the same answer. I made a script for my calculator to find it by summing, but here's a more advanced way to describe the logic:
At x seconds, (where x is an integer) the dog was running at 2^x m/s, accelerates to 2^(x+1) m/s, and has traveled 2^(x+1)-2 m (2^(x+1)-2 is equivalent to the sum of 2^1 ... 2^x and I might've used that instead, but 1. TeX-formatted equations, like I'd need to use the Sigma function, don't spoilerize, and 2. I don't already know the TeX format for Sigma). 2^(x+1)-2 first becomes 500000 or higher during the 18th second, and 2^18=262144, so the dog was running at 262,144 m/s when he passed the 500 km mark. On a side note, I think it took the dog approx. 17.907 seconds to reach the 500 km mark.

Last fiddled with by Mini-Geek on 2009-03-31 at 12:24
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