1. Samochód o masie m = 1200 [kg] porusza się z prędkością v = 45 [km/h]. Jak wielka musi być siła hamująca F, aby mogła zatrzymać ten samochód na drodze
s = 50 [m]?
s = 50 [m]?
Isoko
![Dane:\\m = 1200[kg]\\v = 45 [ \frac{km}{h}] = \frac{45000m}{3600s} = 12,5 [ \frac{m}{s}]\\s = 50[m]\\\\Szukane :\\F = ? \\\\rozwiazanie :\\a = \frac{F}{m}\\F = am \\\\s = \frac{1}{2}at^2 = \frac{1}{2} \frac{\Delta v}{\Delta t} \cdot t^2 \ \ /\cdot 2 \Delta t \\ 2s\Delta t = \Delta v t^2 \ \ / : t^2\\ \frac{ 2s\Delta t }{t^2} = \Delta v ---> \frac{t^2}{ 2s\Delta t } = \frac{1}{\Delta v} \ \ \ /\cdot 2s \\\\ \frac{t^2}{\Delta t} = \frac{1}{\Delta v} \cdot 2s](https://tex.z-dn.net/?f=Dane%3A%5C%5Cm+%3D+1200%5Bkg%5D%5C%5Cv+%3D+45+%5B+%5Cfrac%7Bkm%7D%7Bh%7D%5D+%3D+%5Cfrac%7B45000m%7D%7B3600s%7D+%3D+12%2C5+%5B+%5Cfrac%7Bm%7D%7Bs%7D%5D%5C%5Cs+%3D+50%5Bm%5D%5C%5C%5C%5CSzukane+%3A%5C%5CF+%3D+%3F+%5C%5C%5C%5Crozwiazanie+%3A%5C%5Ca+%3D+%5Cfrac%7BF%7D%7Bm%7D%5C%5CF+%3D+am+%5C%5C%5C%5Cs+%3D+%5Cfrac%7B1%7D%7B2%7Dat%5E2+%3D+%5Cfrac%7B1%7D%7B2%7D+%5Cfrac%7B%5CDelta+v%7D%7B%5CDelta+t%7D+%5Ccdot+t%5E2+%5C+%5C+%2F%5Ccdot+2+%5CDelta+t+%5C%5C+2s%5CDelta+t+%3D+%5CDelta+v+t%5E2+%5C+%5C+%2F+%3A+t%5E2%5C%5C+%5Cfrac%7B+2s%5CDelta+t+%7D%7Bt%5E2%7D+%3D+%5CDelta+v+---%3E+%5Cfrac%7Bt%5E2%7D%7B+2s%5CDelta+t+%7D+%3D+%5Cfrac%7B1%7D%7B%5CDelta+v%7D+%5C+%5C+%5C+%2F%5Ccdot+2s+%5C%5C%5C%5C+%5Cfrac%7Bt%5E2%7D%7B%5CDelta+t%7D+%3D+%5Cfrac%7B1%7D%7B%5CDelta+v%7D+%5Ccdot+2s+ "Dane:\\m = 1200[kg]\\v = 45 [ \frac{km}{h}] = \frac{45000m}{3600s} = 12,5 [ \frac{m}{s}]\\s = 50[m]\\\\Szukane :\\F = ? \\\\rozwiazanie :\\a = \frac{F}{m}\\F = am \\\\s = \frac{1}{2}at^2 = \frac{1}{2} \frac{\Delta v}{\Delta t} \cdot t^2 \ \ /\cdot 2 \Delta t \\ 2s\Delta t = \Delta v t^2 \ \ / : t^2\\ \frac{ 2s\Delta t }{t^2} = \Delta v ---> \frac{t^2}{ 2s\Delta t } = \frac{1}{\Delta v} \ \ \ /\cdot 2s \\\\ \frac{t^2}{\Delta t} = \frac{1}{\Delta v} \cdot 2s")
![-->>>> t = \frac{1}{\Delta v} \cdot 2s\\\\t = \frac{1}{12,5} \cdot 2\cdot 50 = 8[s]\\\\\\a = \frac{\Delta v}{\Delta t} \\a = \frac{12,5}{8} = 1,5625 [ \frac{m}{s^2} ] \\\\\\\\F = 1,5625 [ \frac{m}{s^2} ] \cdot 1200[kg]\\F = 1875 [N] = 1,875[kN]](https://tex.z-dn.net/?f=--%3E%3E%3E%3E+t+%3D+%5Cfrac%7B1%7D%7B%5CDelta+v%7D+%5Ccdot+2s%5C%5C%5C%5Ct+%3D+%5Cfrac%7B1%7D%7B12%2C5%7D+%5Ccdot+2%5Ccdot+50+%3D+8%5Bs%5D%5C%5C%5C%5C%5C%5Ca+%3D+%5Cfrac%7B%5CDelta+v%7D%7B%5CDelta+t%7D+%5C%5Ca+%3D+%5Cfrac%7B12%2C5%7D%7B8%7D+%3D+1%2C5625+%5B+%5Cfrac%7Bm%7D%7Bs%5E2%7D+%5D+%5C%5C%5C%5C%5C%5C%5C%5CF+%3D+1%2C5625+%5B+%5Cfrac%7Bm%7D%7Bs%5E2%7D+%5D+%5Ccdot+1200%5Bkg%5D%5C%5CF+%3D+1875+%5BN%5D+%3D+1%2C875%5BkN%5D "-->>>> t = \frac{1}{\Delta v} \cdot 2s\\\\t = \frac{1}{12,5} \cdot 2\cdot 50 = 8[s]\\\\\\a = \frac{\Delta v}{\Delta t} \\a = \frac{12,5}{8} = 1,5625 [ \frac{m}{s^2} ] \\\\\\\\F = 1,5625 [ \frac{m}{s^2} ] \cdot 1200[kg]\\F = 1875 [N] = 1,875[kN]")
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