Physics of Project Orion I was reading the book "Project Orion" by George Dyson. For those who are unaware, Project Orion was basically a plan to launch a spaceship by flinging bombs out the rear and detonating them. The plasma from the explosion would contact a "pusher plate", which was attached to shock absorbers, which themselves are attached to the main spaceship. The shock absorbers are supposed to turn the 10,000 $g$ sledgehammer from a nuclear bomb into a more manageable 2 $g$ acceleration so the crew doesn't liquify. 
Freeman Dyson says the "peak acceleration on top of a shock absorber is proportional to $\frac{v^2}{L}$ where $v$ is the change in velocity per bomb, and $L$ is the length of the shock absorber. I'd like to know where this formula came from, and I'd also like to know what the constant is. Is the constant just the "k" value of a spring? 
 A: 
I'd like to know where this formula came from...

I am guessing it was an assumption about kinematics where one assumes constant acceleration.  If this is valid, then we know:
$$
V_{f}^{2} - V_{o}^{2} = 2 \ a \ \Delta x \tag{0}
$$
where $V_{i}$ is the speed ($i$ = $f$ for final and $o$ for initial), $a$ is the acceleration, and $\Delta x$ is the displacement.  In the example you gave, we would have $V_{o}$ = 0 so the acceleration would be roughly given by:
$$
a \approx \frac{ V_{f}^{2} }{ 2 \ \Delta x } \tag{1}
$$

...and I'd also like to know what the constant is...

For this, we just use the Hooke's law and Equation 1 to show:
$$
k \approx \frac{ 1 }{ 2 } \ m \ \frac{ V_{f}^{2} }{ \Delta x^{2} } \tag{2}
$$
where $m$ is the mass of the object attached to a massless spring (this latter part is obviously not true, thus the $\approx$ instead of $=$).  Notice that Equation 2 could also be derived from energy conservation as well.
Side Note:  I am hoping the project describe some sort of dampener on such a spring assembly otherwise the spacecraft would be shaking like mad for a long time.  Typically this would add a term $\propto - \gamma \tfrac{ \Delta x }{ \Delta t }$ to the simple harmonic oscillator equation.
