Brain injuries in auto accidents. Brain injuries generally occur any time the brain's acceleration reaches 100 g for even a short time. Consider a car running into a solid barrier. With an airbag, the driver's head moves through a distance of 20 cm while the airbag stops it. Without an airbag, the head continues forward until the seatbelt stops the torso, causing the head to stop in a distance of only 5.0 cm.
a) Find the maximum speed with which the car can strike the barrier without causing brain injury, using an airbag.
b) Find the maximum speed with which the car can strike the barrier without causing brain injury, without using an airbag.