Modern cars are designed with a number of important safety features to protect y

Question

Modern cars are designed with a number of important safety features to protect you in a crash. These include crumple zones, air bags, and seat belts. Consider how a crumple zone (a section of the car that is designed to compress, like an accordion) and a seat belt work together in a head-on collision in which you go from a speed of 35.0 km/h to rest.

(a) If you are not wearing a seat belt, then, in the crash, you generally keep moving forward until you hit something like the windshield. If you come to rest after decelerating through a distance of 8.00 cm after hitting the windshield, what is the magnitude of your average acceleration during the deceleration period?
m/s2

(b) If, instead, you are wearing your seat belt, it keeps you in your seat, and you keep moving forward as the front of the car crumples like an accordion. If the compression of the crumple zone is 75.0 cm, what is the magnitude of your average acceleration during the deceleration period?

Please help and explain how to do it :(

Explanation / Answer

vi = 35 km/h = 35*(5/18) = 9.72 m/s

vf = 0

x = 0.08 m

from the equation of motion

vf^2 - vi^2 = 2*a*x

a = -9.72^2/(2*0.08) = -590.5 m/s^2

deceleration = 509.5 m/s^2

++++++++++

(b)

given = x = 0.75 m

vf = 0

vi = 9.72 m/s

a = vi^2/2x

a = (9.72^2)/(2*0.75)

a = 63.0 m/s^2 <<------answer

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