dane: vo = 20 m/s a = 4 m/s2 s = 300 m szukane: t = ? s = vot + at^2/2 I*2 2s = 2vot + at^2 at^2 + 2vot - 2s = 0 4t^2 + 2 * 20t - 2 * 300 = 0 4t^2 + 40t - 600 = 0 /:4 t^2 + 10t - 150 = 0 Delta = 10^2 - 4 *(-150) = 100 + 600 = 700 VD = V700 = 10V7 = 26,46 t > 0 t = (-10 + 26,46)/2 t = 8,23 s
[latex]Dane:\ v_0=20frac{m}{s}\ s=300m\ a=4frac{m}{s^2}\ Oblicz:\ t=?\ Rozwiazanie:\ s=v_0t+frac{at^2}{2}\\ 2s=2v_0t+at^2\\ 2*300=2*20t+4t^2\\ 600=40t+4t^2\\ 150=10t+t^2\\ t^2+10t-150=0\\ Delta =10^2-4*1*(-150)\ Delta=700\\ sqrt{Delta}=sqrt{700}approx 26,46\\ t_1=frac{-10-26,46}{2}=-18,23\\ t_2=frac{-10+26,46}{2}=8,23s\\ t_1 otin D\ t=t_2=8,23s[/latex] Pozdrawiam, Adam
