The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than 250 m/s2. If you are in an automobile accident with an initial speed of 136 km/h (85 mi/h) and you are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

i am asking for help, i just went as far as converting the km/hr to m/s, and got stuck.

Vo = 136km/h = 136,000m/3600s=37.78 m/s

V^2 = Vo^2 + 2a*d
d = (V^2-Vo^2)/2a
d = (0-(37.78^2))/-500 = 2.85 m.

Well, looks like you need help figuring out the distance the airbag needs to stop you to survive the crash. Let's break it down!

First, let's convert your initial speed from km/h to m/s. Since 1 km/h is equal to 0.2778 m/s, we multiply 136 km/h by 0.2778 to get 37.313 m/s. So, your initial speed is 37.313 m/s.

Now, we know that your acceleration needs to be less than 250 m/s² to survive. Since you're being stopped by the airbag, your final speed will be 0 m/s.

To calculate the distance, we can use the formula:
distance = (final speed² - initial speed²) / (2 * acceleration)

Plugging in the values:
distance = (0² - 37.313²) / (2 * -250)
distance = (-1394.17) / (-500)
distance ≈ 2.788 meters

So, the airbag needs to stop you within approximately 2.788 meters for you to survive the crash. Just a little reminder, make sure you buckle up and drive safely to avoid testing this in real life!

To solve this problem, we can use the equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (which is 0 as you come to a sudden stop)
u = initial velocity (136 km/h)
a = acceleration (250 m/s^2)
s = distance

We need to rearrange the equation to solve for s:

0 = (136 km/h)^2 + 2 * 250 m/s^2 * s

First, let's convert the initial velocity from km/h to m/s:

1 km/h = 1000 m/3600 s = 10/36 m/s

So, u = (136 km/h) * (10/36) m/s = 374.44 m/s

Now, we rearrange the equation:

0 = (374.44 m/s)^2 + 2 * 250 m/s^2 * s

Simplifying further:

0 = 140000 m^2/s^2 + 500 m/s^2 * s

Now, let's isolate the variable s:

500 m/s^2 * s = -140000 m^2/s^2

s = (-140000 m^2/s^2) / (500 m/s^2)

s = -280 m

Since distance cannot be negative, we take the magnitude:

s = 280 m

Therefore, the airbag must stop you over a distance of 280 meters for you to survive the crash.

Ma'am Sanchez for the win!!!

5 × 10ooo