x(t)= 4+3t+2t^3   oblicz:   - V(t), a(t) - x(0), x(2) - V(0), V(2), Vśr (0->2) - a (0), a(2), aśr (0->2)

[latex]x(t) = 2t^3 + 3t + 4 \\ v(t) = frac{dx}{dt} \ v(t) = frac{d}{dt}(2t^3+3t+4) \ v(t) = 6t^2+3 \ \ a(t) = frac{d^2x}{dt^2} \ a(t) = frac{dv}{dt} \ a(t) = frac{d}{dt}(6t^2+3) \ a(t) = 12t \ \ x(0) = 2cdot0^3 + 3cdot0+4 = 4\ x(2) = 2cdot2^3 + 3cdot2+4 = 16+6+4 = 26[/latex]  [latex]\ v(0) = 6cdot0^2+3 = 3 \ v(2) = 6cdot2^2+3 = 24+3 = 27\ a(0) = 12cdot 0 = 0 \ a(2) = 12cdot 2 = 24 \ \ v_{sr} = frac{Delta v}{Delta t} = frac{27-3}{2-0} = frac{24}{2} = 12 \ [/latex] [latex]a_{sr} = frac{Delta a}{Delta t} = frac{24-0}{2-0} = frac{24}{2} = 12 [/latex] Korzystamy ze wzoru na pochodną z wielomianu: [latex]x = ct^n => frac{dx}{dt} = cnt^{n-1} [/latex]