G forces

Calculate deceleration of car (as multiple of gravitational acceleration g = 9.81 m/s²) which occurs when a car in a frontal collision slows down uniformly from a speed 111 km/h to 0 km/h in 1.2 meters trajectory.

Correct result:

G =  40.4 g

Solution:

$$\begin{gathered} s={\displaystyle \frac{1}{2}}a{t}^2=1.2m \\ 2s=a{t}^2 \\ a={\displaystyle \frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}} \\ v=at={\displaystyle \frac{2s}{t}}=111km\mathrm{/}h=30.833m\mathrm{/}s \\ t={\displaystyle \frac{2s}{v}}={\displaystyle \frac{2\cdot 1.2}{30.833}}=0.0778378s \\ a=v\mathrm{/}t=30.833\mathrm{/}0.0778378=396.123m\mathrm{/}{s}^2 \\ G=a\mathrm{/}g=40.4\text{ g} \end{gathered}$$

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