A human being cannot tolerate acceleration of much more than a few hundred m/s2

Question

A human being cannot tolerate acceleration of much more than a few hundred m/s2 without sustaining serious permanent injury. If the acceleration is sustained for more than a few seconds, the maximum tolerable acceleration is much less. Suppose a car is initially moving at 32.7 m/s and then is quickly stopped in a collision.
(a) What is the minimum time over which the driver must be decelerated in order that he not experience an acceleration of magnitude greater than 1.03 102 m/s2? Assume constant acceleration.
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(b) What is the minimum distance the driver must be allowed to move forward during the deceleration? (Air bags are an improvement over seat belts because the distance the driver moves forward is greater with a compressible air bag than with a seat belt. This does not mean, however, that you would want to move forward in the car without air bags.)
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Explanation / Answer

a) if the car decelerates from 32.7 m/s to 0, and the acceleration is 1.03x102, then using

vf = v0 + at

0 = 32.7 + (-103)t ---> t = .3175 sec

b.) Now we use the kinematics formula

x = v0t + (1/2)at2

x = (32.7)(.3175) + .5(-103)(.3175)2 = 5.191 m

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