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.