Brain injuries generally occur any time the brain\'s acceleration reaches 100 g

Question

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 cmwhile 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.Part A Find the maximum speed with which the car can strike the barrier without causing brain injury, using an airbag. Part B Find the maximum speed with which the car can strike the barrier without causing brain injury, without using an airbag .

Explanation / Answer

lets assume the brain acceleration is 100g/cm^2
Due to Newtoms 1st law of motion,that means that the car is also traveling at the acceleration of 100g/cm^2.
(A)With an air bag,the head is 20cm away from the point which when hit,causes brain injury.
But still,the accelaration of the brain which causes acceleration of head=car acceleration(100)
1st,remember that conversion of units is required.
100g/cm^2=1000kg/m^2
20cm=0.2m
Using 3rd equation of motion
V^2=u^2+as
0=u^2+(1000*0.2)
U=14.142136m/s
(since if the car strikes the barrier,the head will continue with the same speed)
(b)v^2=u^2+as
5cm=0.05m
0=u^2+(1000*0.05)
U=7.0710678

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