I like that approach Rolschwarz, I hadnt thought of that one.
Yes, give the stopping distance a value, say 100mm, you can now calculate the impact force = KE / 100mm. Then use this impact force and the same stopping distance (rod deflection) in the deflection equation to calculate a suitable `I` value for the rod. Also check out the rod stress as I outlined previously. You may have to try this approach a few times in order to obtain a suitable rod size that conforms to all the criteria.
Bear in mind that, the smaller the stopping distance chosen, the greater will be the impact force and larger the rod will have to be to resist this. You could also pick a rod size and work backwards through the equations.
A trial and error approach is often an easier way to tackle this sort of problem, if not a bit long winded.