Auto przebylo droge zlozona z 3 odcinkow o dlugosci n.predkosc v1=50km/h,predkosc v2=60km/h.predkosc v3=70km/h.Zjaka srednia predkoscia poruszal sie samochod?
basetla
![v_{sr} = \frac{s_{c}}{t_{c}}\\\\s_{c} = 3n\\t = t_1 + t_2 + t_3 = \frac{n}{v_1}+\frac{n}{v_2}+\frac{n}{v_3}= \frac{n(v_2v_3+v_1v_3+v_1v_2)}{v_1v_2v_3)}\\\\v_{sr} = \frac{3n}{\frac{n(v_2v_3+v_1v_3+v_1v_2)}{v_1v_2v_3}}=\frac{3v_1v_2v_3}{v_2v_3+v_1v_3+v_1v_2}\\\\v_{sr} = \frac{3*50*60*70}{60*70+50*70+50*60} \ [\frac{km}{h}]\\\\v_{sr}\approx58,88\frac{km}{h}](https://tex.z-dn.net/?f=v_%7Bsr%7D+%3D+%5Cfrac%7Bs_%7Bc%7D%7D%7Bt_%7Bc%7D%7D%5C%5C%5C%5Cs_%7Bc%7D+%3D+3n%5C%5Ct+%3D+t_1+%2B+t_2+%2B+t_3+%3D+%5Cfrac%7Bn%7D%7Bv_1%7D%2B%5Cfrac%7Bn%7D%7Bv_2%7D%2B%5Cfrac%7Bn%7D%7Bv_3%7D%3D+%5Cfrac%7Bn%28v_2v_3%2Bv_1v_3%2Bv_1v_2%29%7D%7Bv_1v_2v_3%29%7D%5C%5C%5C%5Cv_%7Bsr%7D+%3D+%5Cfrac%7B3n%7D%7B%5Cfrac%7Bn%28v_2v_3%2Bv_1v_3%2Bv_1v_2%29%7D%7Bv_1v_2v_3%7D%7D%3D%5Cfrac%7B3v_1v_2v_3%7D%7Bv_2v_3%2Bv_1v_3%2Bv_1v_2%7D%5C%5C%5C%5Cv_%7Bsr%7D+%3D+%5Cfrac%7B3%2A50%2A60%2A70%7D%7B60%2A70%2B50%2A70%2B50%2A60%7D+%5C+%5B%5Cfrac%7Bkm%7D%7Bh%7D%5D%5C%5C%5C%5Cv_%7Bsr%7D%5Capprox58%2C88%5Cfrac%7Bkm%7D%7Bh%7D "v_{sr} = \frac{s_{c}}{t_{c}}\\\\s_{c} = 3n\\t = t_1 + t_2 + t_3 = \frac{n}{v_1}+\frac{n}{v_2}+\frac{n}{v_3}= \frac{n(v_2v_3+v_1v_3+v_1v_2)}{v_1v_2v_3)}\\\\v_{sr} = \frac{3n}{\frac{n(v_2v_3+v_1v_3+v_1v_2)}{v_1v_2v_3}}=\frac{3v_1v_2v_3}{v_2v_3+v_1v_3+v_1v_2}\\\\v_{sr} = \frac{3*50*60*70}{60*70+50*70+50*60} \ [\frac{km}{h}]\\\\v_{sr}\approx58,88\frac{km}{h}")
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