auto przebylo droge zlozona z 3 odcinkow o dlugosci n.predkosc v1=50km/h,predkosc v2=60km/h.predkosc v3=70km/h.Zjaka srednia predkoscia poruszal sie samochod?

[latex]dane:\s_1 = s_2 = s_3 = n\v_1 = 50frac{km}{h}\v_2 = 60frac{km}{h}\v_3 = 70frac{km}{h}\szukane:\v_{sr} = ?[/latex] [latex]v_{sr} = frac{s_{c}}{t_{c}}\\s_{c} = 3n\t = t_1 + t_2 + t_3 = frac{n}{v_1}+frac{n}{v_2}+frac{n}{v_3}= frac{n(v_2v_3+v_1v_3+v_1v_2)}{v_1v_2v_3)}\\v_{sr} = frac{3n}{frac{n(v_2v_3+v_1v_3+v_1v_2)}{v_1v_2v_3}}=frac{3v_1v_2v_3}{v_2v_3+v_1v_3+v_1v_2}\\v_{sr} = frac{3*50*60*70}{60*70+50*70+50*60} [frac{km}{h}]\\v_{sr}approx58,88frac{km}{h}[/latex]