1.
[tex]Dane:\\m = 800 \ g = 0,8 \ kg\\v = 54\frac{km}{h} = 54:3,6\frac{m}{s} = 15\frac{m}{s}\\Szukane:\\E_{k} = ?\\\\Rozwiazanie\\\\E_{k} = \frac{mv^{2}}{2}\\\\E_{k} = \frac{0,8 \ kg\cdot(15\frac{m}{s})^{2}}{2}\\\\\boxed{E_{k} = 90 \ J}[/tex]
2.
[tex]Dane:\\m_1= m_2=m\\v_1 = 40\frac{km}{h} = 11,1\frac{m}{s}\\v_2 = 80\frac{km}{h} = 22,2\frac{m}{s}\\Szukane:\\\frac{E_{k_2}}{E_{k_1}} = ?\\\\Rozwiazanie\\\\\frac{E_{k_2}}{E_{k_1}} = \frac{mv_2^{2}}{mv_1^{2}} = \frac{(22,2\frac{m}{s})^{2}}{(11,1\frac{m}{s})^{2}}=(\frac{22,2}{11,1})^{2} = 2^{2} = \boxed{4}[/tex]
Odp. Energia kinetyczna samochodu wzrośnie 4 razy.
3.
[tex]Dane:\\m = 300 \ kg\\v = 5\frac{m}{s}\\Szukane:\\E_{k}=?\\\\Rozwiazanie\\\\E_{k} = \frac{mv^{2}}{2}\\\\E_{k} =\frac{300 \ kg\cdot(5\frac{m}{s})^{2}}{2}\\\\\boxed{E_{k} =3 \ 750 \ J = 3,75 \ kJ}\\\\(1 \ kJ = 1000 \ J)[/tex]
