Question

Un biciclist a plecat din orasul A in orasul B . Prima jumatate de drum a mers cu V1=12 km/h , jumatate din timpul ramas a mers cu V2=8 km / h , iar restul drumului a mers pe jos cu V3= 4 km/h . Calculati viteza medie

Answer 1

[tex]\displaystyle Se~da:\\ \\ v_1=12\frac{km}{h}\\ \\ d_1=\frac d2\\ \\ v_2=8\frac{km}{h}\\ \\ t_2=\frac {t-t_1}2s\\ \\ v_3=4\frac{km}{h}\\ \\ d_3=d-d_1-d_2\\ \\ v=?\frac{km}{h}\\ \\ \\ [/tex]

$\displaystyle Formule:\\ \\ v=\frac{d}{t}\\ \\ \\ t=t_1+t_2+t_3\\ \\ t=t_1+\frac{t-t_1}{2}+t_3\\ \\ 2t=2t_1+t-t_1+2t_3\\ \\ t=t_1+2t_3\\ \\ \\ t_3=\frac{d_3}{v_3}\\ \\ \\ d_3=d-d_1-d_2\\ \\ d_3=d-t_1\times v_1-t_2\times v_2\\ \\ d_3=d-t_1\times v_1-t_2\times v_2\\ \\ d_3=d-t_1\times v_1-\frac{t-t_1}{2}\times v_2$

[tex]\displaystyle d_3=\frac{2d-2\times t_1\times v_1-t\times v_2+t_1\times v_2}{2}\\ \\ \\ t_3=\frac{2d-2\times t_1\times v_1-t\times v_2+t_1\times v_2}{2\times v_3}\\ \\ \\ t=t_1+\frac{2d-2\times t_1\times v_1-t\times v_2+t_1\times v_2}{v_3}\\ \\ t\times v_3=t_1\times v_3+2d-2\times t_1\times v_1-t\times v_2+t_1\times v_2\\ \\ t\times (v_2+v_3)=2d+t_1\times(v_3-2\times v_1+v_2)\\ \\ \\ t_1=\frac{d_1}{v_1}\\ \\ \\ d_1=\frac d2\Rightarrow t_1=\frac{d}{2\times v_1}\\ \\ \\[/tex]


[tex]\displaystyle t\times(v_2+v_3)=2d+\frac{d\times(v_3-2\times v_1+v_2)}{2\times v_1}\\ \\ t\times(v_2+v_3)=\frac{4\times d\times v_1+d\times(v_3-2\times v_1+v_2)}{2\times v_1}\\ \\ t\times(v_2+v_3)=\frac{d\times(4\times v_1+v_3-2\times v_1+v_2)}{2\times v_1}\\ \\ t=\frac{d\times(2\times v_1+v_2+v_3)}{2\times v_1\times(v_2+v_3)}\\ \\ \\ v=\frac{d\times 2\times v_1\times (v_2+v_3)}{d\times (2\times v_1+v_2+v_3)}\\ \\ v=\frac{2\times v_1\times (v_2+v_3)}{2\times v_1+v_2+v_3}\\ \\ \\ [/tex]


[tex]\displaystyle Calcule:\\ \\ v=\frac{2\times 12\times (8+4)}{2\times 12+8+4}=8\frac{km}{h}[/tex]