Optimize Designs for Collision Safety Practice Test

A 60 kg test dummy moves at $v=12\ \text{m/s}$ before hitting a padded wall and stopping. Designers can tune the padding to increase the collision time $\Delta t$. Safety requires the average force to be at most $F_{\max}=1800\ \text{N}$ using $F_{\text{avg}}=\Delta p/\Delta t$. A mechanical constraint limits the maximum achievable collision time to $\Delta t\le 0.50\ \text{s}$. What is the minimum collision time required, and is it achievable?

A 1000 kg car is tested in a crash at $v=18\ \text{m/s}$. Engineers can choose between two crumple-zone designs (single parameter is deformation distance $d$): Design A allows $d=0.50\ \text{m}$, Design B allows $d=0.80\ \text{m}$. The force limit is $F_{\max}=2.5\times 10^5\ \text{N}$ and $F\approx \text{KE}/d$. A packaging constraint requires $d\le 0.85\ \text{m}$. Which design best minimizes force while meeting all constraints?