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. what is the shortest survivable distance over which the driver's head could have come to rest?

0.22 m

Explanation:

We are told that the driver can survive an acceleration of 50g only if the collision lasts no longer than 30 ms. So,

The acceleration is

where the negative sign is due to the fact that this is a deceleration, since the driver comes to a stop in the collision.

First of all, we can find what the initial velocity of the car should be in this conditions by using the equation:

And since the final velocity is zero, v=0, and solving for u,

And now we can find the corresponding distance travelled using the equation: