[latex]v_1=40frac{km}{h}\ v_2=60frac{km}{h}\\ v_{sr}=frac{s_1+s_2}{t_1+t_2}\\ s_1=s_2Rightarrow s_1+s_2=2s\\ v_{sr}=frac{2s}{t_1+t_2}\\ v=frac{s}{t}Rightarrow t=frac{s}{v}[/latex] [latex]v_{sr}=frac{2s}{frac{s}{v_1}+frac{s}{v_2}}\\ v_{sr}=frac{2}{frac{1}{v_1}+frac{1}{v_2}}\\ v_{sr}=frac{2}{frac{v_2}{v_1v_2}+frac{v_1}{v_1v_2}}\\ v_{sr}=frac{2}{frac{v_1+v_2}{v_1v_2}}\\ v_{sr}=frac{2v_1v_2}{v_1+v_2}\\ v_{sr}=frac{2*60*40}{60+40}\\ v_{sr}=frac{4800}{100}\\ v_{sr}=48frac{km}{h}[/latex] Pozdrawiam, Adam
dane: s1 = s/2 v1 = 40 km/h s2 = s/2 v2 = 60 km/h szukane: vśr = ? vśr = s/t t = t1 + t2 t = s/v t = s1/v1 + s2/v2 = s/2 : v1 + s/2 : v2 = s/2v1 + s/2v2 = (sv1 + sv2)/2v1v2 = = s(v1 + v2)/2v1v2 vśr = s : s(v1 + v2)/2v1v2 = s * 2v1v2/[s(v1 + v2)] vśr = 2v1v2/(v1+v2) vśr = 2 * 40 * 60/(40 + 60) = 4800/100 vśr = 48 km/h
