In a car crash, large accelerations of the head can lead to severe injuries or even death. A driver can probably survive an acceleration of 50g that lasts for less than 30 ms, but in a crash with a 50g acceleration lasting longer than 30 ms, a driver is unlikely to survive. Imagine a collision in which a driver’s head experienced a 50g acceleration. 

a. What is the highest speed that the car could have had such that the driver survived? 

b. What is the shortest survivable distance over which the driver’s head could have come to rest?