I was using:
d = (1/2)at2
and somehow got a travel distance of only one kilometer after 604,800 seconds (1 week). But now I'm getting 10,584 km, still woefully inadequate to get you to Mars in a reasonable amount of time.
'Course, in reality, the initial velocity isn't zero either. So it's not as bad as I'm making it out to be. But still, he's going to have to scale up the power of his invention by a factor of much, much more than a billion.
More power to him.
Using d = at2/2, an acceleration of 35e-3 m/sec2, and t = 604,800 sec, you get a distance travelled of 6.4 million kilometers in one week.