Scriem x ca o functie de t:
[tex] x(t)=10+2t+5t^2 [/tex]
Setand prima derivata fata de timp a acestei functii, avem:
[tex] v=\dot{x}=\dfrac{dx}{dt}=\dfrac{d}{dt}(10+2t+5t^2)=10t+2 [/tex]
Astfel, viteza initiala este data de:
[tex] v=v(0)=2 m/s [/tex]
Derivata a doua a functiei x(t) ne va da expresia acceleratiei:
[tex] a=\ddot{x}=\dfrac{d}{dt}\left(\dfrac{d}{dt}10+2t+5t^2\right) [/tex]
[tex] \implies a=\dfrac{dv}{dt}=\dfrac{d}{dt}(10t+2)=10+0=10 m/s^2[/tex]
Legea vitezei:
[tex] v(t)=v_0+at=2+10t [/tex]
