Surviving a Car Crash with Airbag Deployment: Calculating Stopping Distance

[courtrigrad]

The human body can survive a negative acceleration trauma incident if the magnitude of the acceleration is less than 250 m/s^2. If you are in an automobile accident at an initial speed of 96 km/h and 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 know that $v_{0} = 96$, $v_{x} = 0$ and $a_{x} = 250$. So is it correct to say $v_{x} = v_{x}_{0} + a_{x}t$ to find the time, or $0 = 96-250t$ and $t = 0.384 sec$? Then you use $x-x_{0} = v_{x}_{0}t + \frac{1}{2}a_{x}t^{2}$ and you get the distance to be $18.432 m$

Is this correct?

Thanks

 

[courtrigrad]

any ideas?

 

[Leong]

change 96 km/h to m/s.

 

[Jameson]

I would do the above suggestion and use this equation... it's faster.

$$V_{f}^2=V_{0}^2+2ad$$

 

[courtrigrad]

A car 3.5 m in length and traveling at a constant speed of 20 m/s is approaching an intersection. The width of the intersection is 20 m. The light turns yellow when the front of the car is 50 m from the beginning of the intersection. If the driver steps on the brake, the car will slow at -4.2 m/s^2. If the driver instead steps on the gas pedal, the car will accelerate at 1.5 m/s^2. The light will be yellow for 3.0 s. Ignore the reaction time of the driver. To avoid being in the intersection while the light is red, should the driver hit the brake pedal or gas pedal?

Could someone give me a general idea of where to start, and a general problem solving strategy?

Thanks