Answer:
a) The severity index (SI) is 3047.749, b) The injured travels 0.345 meters during the collision.
Explanation:
a) The g-multiple of the acceleration, that is, a ratio of the person's acceleration to gravitational acceleration, is:
![a' = \frac{35\,\frac{m}{s^{2}} }{9.807\,\frac{m}{s^{2}} }](https://tex.z-dn.net/?f=a%27%20%3D%20%5Cfrac%7B35%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%7D%7B9.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%7D)
![a' = 3.569](https://tex.z-dn.net/?f=a%27%20%3D%203.569)
The time taken for the injured to accelerate to final speed is given by this formula under the assumption of constant acceleration:
![v_{f} = v_{o} + a \cdot t](https://tex.z-dn.net/?f=v_%7Bf%7D%20%3D%20v_%7Bo%7D%20%2B%20a%20%5Ccdot%20t)
Where:
- Initial speed, measured in meters per second.
- Final speed, measured in meter per second.
- Acceleration, measured in
.
- Time, measured in seconds.
![t = \frac{v_{f}-v_{o}}{a}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bv_%7Bf%7D-v_%7Bo%7D%7D%7Ba%7D)
![t = \frac{\left(12\,\frac{km}{h} \right)\cdot \left(1000\,\frac{m}{km} \right)\cdot \left(\frac{1}{3600}\,\frac{h}{s} \right)}{35\,\frac{m}{s^{2}} }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Cleft%2812%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20%5Cleft%281000%5C%2C%5Cfrac%7Bm%7D%7Bkm%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B3600%7D%5C%2C%5Cfrac%7Bh%7D%7Bs%7D%20%20%5Cright%29%7D%7B35%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%7D)
![t = 0.095\,s](https://tex.z-dn.net/?f=t%20%3D%200.095%5C%2Cs)
Lastly, the severity index is now determined:
![SI = \frac{a'^{5}}{2\cdot t}](https://tex.z-dn.net/?f=SI%20%3D%20%5Cfrac%7Ba%27%5E%7B5%7D%7D%7B2%5Ccdot%20t%7D)
![SI = \frac{3.569^{5}}{2\cdot (0.095\,s)}](https://tex.z-dn.net/?f=SI%20%3D%20%5Cfrac%7B3.569%5E%7B5%7D%7D%7B2%5Ccdot%20%280.095%5C%2Cs%29%7D)
![SI = 3047.749](https://tex.z-dn.net/?f=SI%20%3D%203047.749)
b) The initial and final speed of the injured are
and
, respectively. The travelled distance can be determined from this equation of motion:
![v_{f}^{2} = v_{o}^{2} + 2\cdot a \cdot \Delta s](https://tex.z-dn.net/?f=v_%7Bf%7D%5E%7B2%7D%20%3D%20v_%7Bo%7D%5E%7B2%7D%20%2B%202%5Ccdot%20a%20%5Ccdot%20%5CDelta%20s)
Where
is the travelled distance, measured in meters.
![\Delta s = \frac{v_{f}^{2}-v_{o}^{2}}{2\cdot a}](https://tex.z-dn.net/?f=%5CDelta%20s%20%3D%20%5Cfrac%7Bv_%7Bf%7D%5E%7B2%7D-v_%7Bo%7D%5E%7B2%7D%7D%7B2%5Ccdot%20a%7D)
![\Delta s = \frac{\left(5.278\,\frac{m}{s} \right)^{2}-\left(1.944\,\frac{m}{s} \right)^{2}}{2\cdot \left(35\,\frac{m}{s^{2}} \right)}](https://tex.z-dn.net/?f=%5CDelta%20s%20%3D%20%5Cfrac%7B%5Cleft%285.278%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D-%5Cleft%281.944%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D%7D%7B2%5Ccdot%20%5Cleft%2835%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%7D)
.