1.
[tex]Dane:\\t = 2 \ min = 2\cdot60 \ s = 120 \ s=\frac{120}{3600} \ h = \frac{1}{30} \ h\\s = 4 \ km\\Szukane:\\v = ?\\\\Rozwiazanie\\\\v = \frac{s}{t}\\\\v = \frac{4 \ km}{\frac{1}{30} \ h} = 120\frac{km}{h}\\\\120\frac{km}{h} = 120\cdot\frac{1000 \ m}{3600 \ s} =33\frac{1}{3} \ \frac{m}{s}\\\\\boxed{v = 120\frac{km}{h} = 33\frac{1}{3} \ \frac{m}{s}}[/tex]
2.
[tex]Dane:\\s = 2 \ km\\v = 60\frac{km}{h}\\Szukane:\\t = ?\\\\Rozwiazanie\\\\v = \frac{s}{t} \ \ \rightarrow \ \ t = \frac{s}{v}\\\\t = \frac{2 \ km}{60\frac{km}{h}} = \frac{2}{60} \ h\\\\\boxed{t = 2 \ min}[/tex]
3.
[tex]Dane:\\t_1 = 1 \ h\\v_1 = 60\frac{km}{h}\\t_2 = 30 \ min = 0,5 \ h\\v_2 = 90\frac{km}{h}\\Szukane:\\v_{sr} = ?\\\\Rozwiazanie\\\\v_{sr} = \frac{s_{c}}{t_{c}}\\\\s = v\cdot t\\\\s_{c} = s_1+s_2 = v_1\cdot t_1 + v_2\cdot t_2 = 60\frac{km}{h}\cdot 1 \ h + 90\frac{km}{h}\cdot0,5 \ h =60 \ km+45 \ km = 105 \ km\\\\t_{c} = t_1+t_2 = 1 \ h + 0,5 \ h = 1,5 \ h\\\\\\v_{sr} = \frac{105 \ km}{1,5 \ h}\\\\\boxed{v_{sr} = 70\frac{km}{h}}[/tex]
4.
[tex]Dane:\\s = 280 \ km\\v_1 = 60\frac{km}{h}\\v_2 = 80\frac{km}{h}\\Szukane:\\t = ?\\\\Rozwiazanie[/tex]
Samochody poruszają się z różną prędkością, więc w tym samym czasie pokonają różne drogi.
[tex]s = s_1 + s_2\\\\v = \frac{s}{t} \ \ \rightarrow \ \ s = v\cdot t\\\\s = v_1\cdot t+v_2\cdot t\\\\s = t(v_1+v_2) \ \ \ |:(v_1+v_2)\\\\t = \frac{s}{v_1+v_2}\\\\t = \frac{280 \ km}{60\frac{km}{h}+80\frac{km}{h}} = \frac{280 \ km}{140\frac{km}{h}}\\\\\boxed{t = 2 \ h}[/tex]
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Verified answer
1.
[tex]Dane:\\t = 2 \ min = 2\cdot60 \ s = 120 \ s=\frac{120}{3600} \ h = \frac{1}{30} \ h\\s = 4 \ km\\Szukane:\\v = ?\\\\Rozwiazanie\\\\v = \frac{s}{t}\\\\v = \frac{4 \ km}{\frac{1}{30} \ h} = 120\frac{km}{h}\\\\120\frac{km}{h} = 120\cdot\frac{1000 \ m}{3600 \ s} =33\frac{1}{3} \ \frac{m}{s}\\\\\boxed{v = 120\frac{km}{h} = 33\frac{1}{3} \ \frac{m}{s}}[/tex]
2.
[tex]Dane:\\s = 2 \ km\\v = 60\frac{km}{h}\\Szukane:\\t = ?\\\\Rozwiazanie\\\\v = \frac{s}{t} \ \ \rightarrow \ \ t = \frac{s}{v}\\\\t = \frac{2 \ km}{60\frac{km}{h}} = \frac{2}{60} \ h\\\\\boxed{t = 2 \ min}[/tex]
3.
[tex]Dane:\\t_1 = 1 \ h\\v_1 = 60\frac{km}{h}\\t_2 = 30 \ min = 0,5 \ h\\v_2 = 90\frac{km}{h}\\Szukane:\\v_{sr} = ?\\\\Rozwiazanie\\\\v_{sr} = \frac{s_{c}}{t_{c}}\\\\s = v\cdot t\\\\s_{c} = s_1+s_2 = v_1\cdot t_1 + v_2\cdot t_2 = 60\frac{km}{h}\cdot 1 \ h + 90\frac{km}{h}\cdot0,5 \ h =60 \ km+45 \ km = 105 \ km\\\\t_{c} = t_1+t_2 = 1 \ h + 0,5 \ h = 1,5 \ h\\\\\\v_{sr} = \frac{105 \ km}{1,5 \ h}\\\\\boxed{v_{sr} = 70\frac{km}{h}}[/tex]
4.
[tex]Dane:\\s = 280 \ km\\v_1 = 60\frac{km}{h}\\v_2 = 80\frac{km}{h}\\Szukane:\\t = ?\\\\Rozwiazanie[/tex]
Samochody poruszają się z różną prędkością, więc w tym samym czasie pokonają różne drogi.
[tex]s = s_1 + s_2\\\\v = \frac{s}{t} \ \ \rightarrow \ \ s = v\cdot t\\\\s = v_1\cdot t+v_2\cdot t\\\\s = t(v_1+v_2) \ \ \ |:(v_1+v_2)\\\\t = \frac{s}{v_1+v_2}\\\\t = \frac{280 \ km}{60\frac{km}{h}+80\frac{km}{h}} = \frac{280 \ km}{140\frac{km}{h}}\\\\\boxed{t = 2 \ h}[/tex]