Explorer Power Gain Problem

[Brian Mansur <bmansur@oc.edu>]

>From Brian

Kelly, I was looking over your explorer paper and the power section, trying 
to understand how you got a power gain of 1E9 W per second.  Your equation 
went something like:

P = F dx/dt = m*a*dx/dt

The mass of the ship was 100E6 kg.  The acceleration was 10m/s^2.  The 
duration of acceleration was 1E7 seconds.  You plugged in the numbers like 
this:

100E6kg * 10m/s^2 * 5m/s = 5E9W

Where did that 5m/s come from.  I thought dx/dt was a distance traveled in 
one second.  My physics textbook tells me power is F * v where v is 
velocity.  Since our average speed is 5E7 m/s (average between our terminal 
speed of 1E8 m/s and 0 m/s) the equation should look like this:

100E6kg * 10m/s^2 * 5E7m/s = 5E16W.

If I'm right, that is a hefty difference in power gain which we couldn't 
hope to meet without loading tremendous amounts of fusion fuel.  Please tell 
me that I'm the one who is wrong.  Also, when I ran the numbers for K.E. 
using the relativity equation and the basic physics equation (these are on 
your explorer paper and I don't have time to write them here) I came up with 
a 100+ fold difference in power.  Can you confirm this?  Do you even have 
time to read this letter? :)