# Pre účinnosť

Pre účinnosť bŕzd osobného vozidla je predpísané, že automobil pohybujúci sa po vodorovnej vozovke rýchlosťou 40km. H musí zastaviť na dráhe 15,4 m. Aké veľké je pritom spomalenie automobilu?

Result

a =  4.008 m/s2

#### Solution:

$v=40 \ km/h=40 / 3.6 \ m/s=11.11111 \ m/s \ \\ s=15.4 \ \text{m} \ \\ \ \\ s=\dfrac{ 1 }{ 2 } a t^2 \ \\ \ \\ v=at \ \\ s=\dfrac{ 1 }{ 2 } a (v/a)^2 \ \\ \ \\ 2 \ s=v^2/a \ \\ \ \\ a=v^2 / (2 \cdot \ s)=11.1111^2 / (2 \cdot \ 15.4) \doteq 4.0083 \doteq 4.008 \ \text{m/s}^2$

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