Question

O maşină se deplaseaza ,o jumatate din drum cu viteza de 80km/h un sfert cu 50km/h si ce a ramas cu 100km/h.Calculati viteza medie​ vreau si rezolvarea​

Answer 1

fie d lungimea totala a drumului

[tex]d_1=\frac{d}{2}\\ d_2=\frac{d}{4}\\d=d_1+d_2+d_3\\ d_3=d-d_1-d_2=d-\frac{d}{2}-\frac{d}{4}=\frac{d}{4}\\ t=t_1+t_2+t_3\\ t_1=\frac{d_1}{v_1}=\frac{d}{2v_1}\\t_2= \frac{d_2}{v_2}=\frac{d}{4v_2}\\ t_3=\frac{d_3}{v_3}=\frac{d}{4v_3}\\ d=v_m*t=>v_m=\frac{d}{t}=\frac{d}{\frac{d}{2v_1}+ \frac{d}{4v_2}+ \frac{d}{4v_3} }=\frac{1}{\frac{2v_2v_3}{4v_1v_2v_3} +\frac{v_1v_3}{4v_1v_2v_3} +\frac{v_1v_2}{4v_1v_2v_3} } =\frac{1}{\frac{2v_2v_3+v_1v_3+v_1v_2}{4v_1v_2v_3} } =\frac{4v_1v_2v_3}{2v_2v_3+v_1v_3+v_1v_2}[/tex]

$v_m=\frac{4v_1v_2v_3}{2v_2v_3+v_1v_3+v_1v_2}=\frac{4*80*50*100}{2*50*100+80*100+80*50}=\frac{1600000}{22000}=72,72 km/h\\v_m=72,72 km/h$