BIO Air-Bag Injuries.? During an auto accident, the vehicle’s air bags deploy and slow down the passengers more gently than if they had hit the windshield or steering wheel. According to safety standards, air bags produce a maximum acceleration of 60 g that lasts for only 36 ms (or less). How far (in meters) does a person travel in coming to a complete stop in 36 ms at a constant acceleration of 60 g?
Solution 25E Step 1: According to Newton’s equations of motion, v = u + at Where, v - Final velocity of the body u - initial velocity of the body a - acceleration of the body t - time of travel Here, they have provided, the maximum acceleration of the airbag is 60 g and it will last for 36 ms. Therefore, a = - 60 g (Since it slows down the body, it will be opposite to the gravitational force. Hence , we should put a minus sign) 2 g = 9.8 m/s 2 2 therefore , a = -60× 9.8 m/s = - 588 m/s t = 36 ms 1 ms = 1/1000 seconds Therefore, t = 36 × (1/1000) seconds = 36 × 10 seconds Once the passenger reaches the ground, the velocity will be zero. Therefore, final velocity, v = 0 m/s Putting all these values in the above equation, we get, 0 = u - ( 588 m/s × 36 × 10 seconds)-3 2 -3 Rearranging the equation, u = ( 588 m/s × 36 × 10 seconds) = 21.17 m/s