s₁ = 0,4 s v₁ = 72 km/h = 20 m/s v₂ = 54 km/h = 15 m/s s₂ = 0,6 s [latex]v_{sr} = frac{s_c}{t_c}\ [/latex] tc = t₁ + t₂ t₁ = s₁/v₁ t₂ = s₂/v₂ [latex]v_{sr} = frac{s_1 + s_2}{t_1 + t_2}\ v_{sr} = frac{s}{frac{s_1}{v_1} + frac{s_2}{v_2}}\ v_{sr} = frac{s}{frac{s_1v_2}{v_1v_2} + frac{s_2v_1}{v_1v_2}}\ [/latex] [latex]v_{sr} = frac{s}{frac{s_1v_2 + s_2v_1}{v_1v_2}}\ v_{sr} = frac{sv_1v_2}{s_1v_2 + s_2v_1}\ v_{sr} = frac{sv_1v_2}{0,4sv_2 + 0,6sv_1}\ v_{sr} = frac{sv_1v_2}{s(0,4v_2 + 0,6v_1)}\ [/latex] [latex]v_{sr} = frac{v_1v_2}{0,4v_2 + 0,6 v_1}\ v_{sr} = frac{20 frac{m}{s} cdot 15frac{m}{s}}{0,4 cdot 15 frac{m}{s} + 0,6 cdot 20 frac{m}{s}} = frac{300 frac{m^2}{s^2}}{6 frac[m}{s} + 12 frac{m}{s} } = 16,67 frac{m}{s}\[/latex]
dane: s1 = 0,4 s v1 = 72 km/h s2 = 0,6 s v2 = 54 km/h szukane: vśr = ? vśr = s/t t = t1+t2 t = s/v t1 = s1/v1 = 0,4s/72 = 0,1s/18 [h] t2 = s2/v2 = 0,6s/54 = 0,1s/9 [h] t = 0,1s/18 + 0,1s/9 = 0,1s/18 + 0,2s/18 = 0,3s/18 = 0,1s/6 [h] vśr = s : 0,1s/6 = 6/0,1 [km/h] vśr = 60 km/h ============ Odp.Średnia prędkość motocyklisty wynosi 60 km/h.
