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I'm attempting to approach this using the identity $$F/A = I/c$$ I can solve for Area easily enough $$A = F(c/I)$$ and I know the distance $d$ is $$d=1/2(at^2)$$

But I'm having difficulty trying to relate this to the time it would take to reach mars.

Any ideas where to go from here?

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I think the first step is to write your last expression as an equation: $d = \frac{1}{2}at^2$. Which variables in this equation are known, and which are the unknown(s)? –  Nathaniel May 15 '13 at 4:12
In a realistic assessment of this you can't use the naive constant acceleration rule because (1) you have to arrive stopped with respect to Mars which means you can't accelerate the whole way, but also can't accelerate half way, (2) it's an orbital problem in which the Sun, Earth, the Moon, Jupiter and Mars are yanking you around all the way, and (3) the intensity is a function of distance (though a lot of that washes out in the orbital dynamics). But assume you are not asking for a realistic assessment. –  dmckee May 15 '13 at 4:19
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You've done the two hard parts: (1) relate area to force and intensity and (2) relate distance, acceleration, and time. For connecting these two, I suggest looking at Newton's second law.

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