Дано:
$v_{1}$ = 60 км/ч;
$v_{2}$ = 10 м/с.
Найти:
$v_{ср}$ − ?
СИ:
$v_{1} = \frac{60 * 1000}{3600} = 16,7$ м/с;
Решение:
$t_{1} = \frac{S}{v_{1}}$;
$t_{2} = \frac{S}{v_{2}}$;
$t = t_{1}+t_{2} = \frac{S}{v_{1}} + \frac{S}{v_{2}} = \frac{Sv_{2}+Sv_{1}}{v_{1}v_{2}} = \frac{S(v_{2}+v_{1})}{v_{1}v_{2}}$;
$v_{ср} = \frac{2S}{t} = \frac{2S}{\frac{S(v_{2}+v_{1})}{v_{1}v_{2}}} = \frac{2Sv_{1}v_{2}}{S(v_{2}+v_{1})}=\frac{2v_{1}v_{2}}{(v_{2}+v_{1})}$;
$v_{ср} = \frac{2 * 16,7 * 10}{16,7 + 10} = 12,5$ м/с.
Ответ: 12,5 м/с.