Problem 1.20

A radius vector of a particle varies with time $t$ as $\mathrm{r}$ $=$ at $(1-\alpha t),$ where a is a constant vector and $\alpha$ is a positive factor. Find: (a) the velocity $\mathbf{v}$ and the acceleration $\mathbf{w}$ of the particle as functions of time; (b) the time interval $\Delta t$ taken by the particle to return to the initial points, and the distance $s$ covered during that time.