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

Answer

`[vec(b) (1 - 2 alpha t), - 2 alpha vec(b), 1//alpha, b//2 alpha]`