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**1. Homework Statement**

During an auto accident, the vehicle's air bags deploy and slowdown the passengers more gently than if they had hit the windshieldor steering wheel. According to safety standards, the bags producea maximum acceleration of 60, but lasting for only 36 (or less).

How far (in meters) does a person travel in coming to a completestop in 36 at a constant accelerationof 60?

**2. Homework Equations**

s=1/2a(t)^2

**3. The Attempt at a Solution**

What I first did was analyze what I have. I know I have an acceleration of -588m/s^2 ( due to the a

_{x}=-g) also I have the time which is 0.036s.

I initially wanted to use the forumula vx

^{2}=v

_{0}x

^{2}+2a

_{x}(x-x

_{0})

Here is where I constantly get confused in these types of problems I know one of the velocities is going to be zero but how do I know which one to make zero.

So what I wanted to do was aquire one of the velocities using v

_{x}=v

_{0}x+at. Then plug it into the above equation however the solution manual chose to use the following equation s=1/2a(t)^2.

Can someone explain to me why my thought process is wrong and why, and how they aquired the above equation.

Thank you