Question

1,exprimati componentele vectorului viteza in functie de componentele vectorului de pozirtie
2,exprimati componentele vectorului acceleratie in functie de componentele vectorului de pozirtie

Answer 1

$\vec{r}(t)=r_x(t)\vec{i}+r_y(t)\vec{j}+r_z(t)\vec{k}$

$\vec{v}\equiv \dfrac{d\vec{r}}{dt}=\left(\dfrac{dr_x}{dt}\right)\vec{i}+\left(\dfrac{dr_y}{dt}\right)\vec{j}+\left(\dfrac{dr_z}{dt}\right)\vec{k}$

$\vec{a}\equiv \dfrac{d^2\vec{r}}{dt^2}=\left(\dfrac{d^2r_x}{dt^2}\right)\vec{i}+\left(\dfrac{d^2r_y}{dt^2}\right)\vec{j}+\left(\dfrac{d^2r_z}{dt^2}\right)\vec{k}$

Asadar componentele pot fi exprimate asa:

$v_{x,y,z}=\dfrac{dr_{x,y,z}}{dt}\\\\a_{x,y,z}=\dfrac{d^2r_{x,y,z}}{dt^2}$