# The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than [closed]

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 auto- mobile accident with an initial speed of 105 km/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?

So, I modeled the problem with this diagram:

It says that the initial position is $$0m$$ and initial velocity is $$29.2\frac{m}{s}$$. After $$t'$$ time has passed, the car crashes; it has traveled a distance of $$X$$, and since it crashed, velocity is 0.

Acceleration is fixed at its maximum value, which is $$250 \frac{m}{s²}$$

Now, I use this formula to obtain $$X$$: $$v_x^2=v_{0x}^2+2a_x\left(x-x_0\right)$$

replacing, I get

$$0,00\,\frac{m}{s} = 852.6\,\frac{m²}{s²}+500\,\frac{m}{s²}X$$ so I solve for X:

$$X = \frac{-852.6\,\frac{m²}{s²}}{500\,\frac{m}{s²}} = -1.70\,m$$

But it's kind of weird that I get a negative distance, so I check the solutions manual; what I get is that $$1.70$$ is correct, but direction is wrong (the negative sign):

The reason is that they choose a negative acceleration, but I don't get why. Could you explain to me why it has to be chosen negative?

## closed as off-topic by ZeroTheHero, Ben Crowell, Aaron Stevens, John Rennie, Jon CusterJan 18 at 14:21

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – ZeroTheHero, Ben Crowell, Aaron Stevens, John Rennie, Jon Custer
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• Don't get all "hung up" on the negative sign. This is physics, not math. – David White Jan 18 at 1:31
• I've added the homework-and-exercises tag. In the future, please use this tag on this type of question. – Ben Crowell Jan 18 at 4:12