Question

Un tren parcurge prima jumatate de drum cu viteza constanta,de n ori mai mare decat viteza cu care parcurge restul drumului. Cunoscand viteza medie (Vm=43,2 km/h si n=1,5),sa se calculeze vitezele v1 si v2.
Vreau si desen!!!

Answer 1

Prima jumatate o parcurge cu viteza v1=nv2(1),iar a doua jumatate cu viteza v2.

$v med= \frac{d}{t}$

d=d1+d2
$d1=d2=\frac{d}{2}$
t=t1+t2

$t1=\frac{d1}{v1}=\frac{\frac{d}{2}}{v1}=\frac{d}{2v1}$


$t2=\frac{d2}{v2} =\frac{\frac{d}{2}}{v2}=\frac{d}{2v2}$



$v med=\frac{d}{\frac{d}{2v1}+\frac{d}{2v2}}$



$vmed=\frac{d}{\frac{d(v1+v2)}{2v1v2}}$


$vmed=\frac{2dv1v2}{d(v1+v2)}$


$vmed=\frac{2v1v2}{v1+v2}$ (2)

Inlocuim relatia (1) in relatia (2) :

$v med=\frac{2nv2^2}{nv2+v2}=\frac{2nv2^2}{v2(n+1)}$

v med v2(n+1)=2nv2²
v med(n+1)=2nv2

$v2=\frac{v med(n+1)}{2n}$

v2=36km/h
v1=54km/h

Answer 2

Ia si cu desen

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