$\text{Dane:}$  

$\text{v}=72\frac{\text{km}}{\text{h}}=72\cdot \frac{1000\text{m}}{3600\text{s}}=20\frac{\text{m}}{\text{s}}$  

${\text{s}}_{\text{l}}=80\text{m}$  

${\text{s}}_{\text{z}}=50\text{m}$  

$\text{Szukane:}$  

${\text{a}}_{\text{l,}}{\text{a}}_{\text{z}}=\text{?}$   

Opóźnienie dla opon letnich:

${\text{s}}_{\text{l}}=\frac{{\text{a}}_{\text{l}}\cdot {\text{t}}_{\text{l}}}{2}$  

Nie mamy czasu, więc obliczamy do ze wzoru:

${\text{a}}_{\text{l}}=\frac{\text{v}}{{\text{t}}_{\text{l}}}\text{/}\cdot {\text{t}}_{\text{l}}$  

${\text{a}}_{\text{l}}\cdot {\text{t}}_{\text{l}}=\frac{\text{v}\cdot \sout{{\text{t}}_{\text{l}}}}{\sout{{\text{t}}_{\text{l}}}}$  

${\text{a}}_{\text{l}}\cdot {\text{t}}_{\text{l}}=\text{v}{\text{/: a}}_{\text{l}}$  

$\frac{\sout{{\text{a}}_{\text{l}}}\cdot {\text{t}}_{\text{l}}}{\sout{{\text{a}}_{\text{l}}}}=\frac{\text{v}}{{\text{a}}_{\text{l}}}$  

${\text{t}}_{\text{l}}=\frac{\text{v}}{{\text{a}}_{\text{l}}}$  

Teraz wstawiamy ten wzór do wzostu na drogę:

${\text{s}}_{\text{l}}=\frac{{\sout{\text{a}}}_{\text{l}}\cdot \frac{{\text{v}}^2}{{\text{a}}_{\text{l}}^{\sout{2}}}}{2}$  

${\text{s}}_{\text{l}}=\frac{{\text{v}}^2}{2\cdot {\text{a}}_{\text{l}}}\text{/}\cdot \left(2\cdot {\text{a}}_{\text{l}}\right)$  

${\text{s}}_{\text{l}}\cdot 2\cdot {\text{a}}_{\text{l}}=\frac{{\text{v}}^2\cdot \sout{2\cdot {\text{a}}_{\text{l}}}}{\sout{2\cdot {\text{a}}_{\text{l}}}}$  

${\text{s}}_{\text{l}}\cdot 2\cdot {\text{a}}_{\text{l}}={\text{v}}^2\text{/: (2}\cdot {\text{s}}_{\text{l}})$  

$\frac{\sout{2\cdot {\text{s}}_{\text{l}}}\cdot {\text{a}}_{\text{l}}}{\sout{2\cdot {\text{s}}_{\text{l}}}}=\frac{{\text{v}}^2}{2\cdot {\text{s}}_{\text{l}}}$  

${\text{a}}_{\text{l}}=\frac{{\text{v}}^2}{2\cdot {\text{s}}_{\text{l}}}$  

Podstawiamy dane liczbowe:

${\text{a}}_{\text{l}}=\frac{{\left(20\frac{\text{m}}{\text{s}}\right)}^2}{2\cdot 80\text{m}}$  

${\text{a}}_{\text{l}}=2,5\frac{\text{m}}{{\text{s}}^2}$            

Teraz obliczamy z wyprowadzonego wyżej wzoru opóźnienie dla opon zimowych:

${\text{a}}_{\text{z}}=\frac{{\text{v}}^2}{2\cdot {\text{s}}_{\text{z}}}=\frac{{\left(20\frac{\text{m}}{\text{s}}\right)}^2}{2\cdot 50\text{m}}$  

${\text{a}}_{\text{z}}=4\frac{\text{m}}{{\text{s}}^2}$  

Odpowiedź: Opóźnienie samochodu w przypadku zastosowania opon letnich wynosi 2,5 m/s², a po zastosowaniu opon zimowych 4 m/s².