Physics
There are many physics components that Aerogels seem to be involved in.
The classic example is a large mass pushing down on the Aerogel and not destroying it. This proves it's resilience to large forces, exceeding the force it exerts back in relation to its own mass. Remember, Force equals mass times acceleration. Since gravity is our acceleration, the force of the car on the Aerogel is equal to the force of the Aerogel on the car (Equal and opposite forces to provide a state of equilibrium).
Scientists are also experimenting with aerogel in regards to the absorption of forces, such as kinetic energy.
http://stardust.jpl.nasa.gov/photo/aerogel.html
Another interesting Physics principle comes from the image to the right. This displays the tracking of small objects that enter the aerogel. These items can travel 6 times or greater than the speed of a bullet. By knowing the frictional resistance and size of the particle, the speed of said object could potentially be solved. However, the importance of capturing these items is more for research than solving physics.