It’s time to write about Mythbusters again! Last night on the show, the team tested a myth that balloons can take the place of an air bag in the front seat of your car, and if you have the right configuration of balloons, you’ll be protected from the damaging effects of a crash.

If you watched the show, you’ll know that this myth was thoroughly busted. The maximum acceleration a human body can take and still survive is \(100g = \SI{980}{m/s^2}\), and no matter what configuration of balloons they tried, they were unable to reduce the acceleration to any less than about \(120g\). This got me thinking about why that might be the case. Physically, keeping a body’s acceleration below a certain threshold is just a matter of spreading that acceleration out over a long enough distance. It’s easy to see that by looking at the relevant equation:

For a car crash, you’d be given \(v_0\), the initial speed, and \(v = 0\), the final speed, and so if you want \(a\) to be small, you have to make \(\Delta x\) large. Specifically,