Question

position vector of a particle is given by \(\sf r = r_0(1-at)t\) , where t is the time and a as well as \(\sf r_0\) are constant. How much distance is covered by the particle in returning to the starting point?

Answer 1

suggest you start with a drawing, this is a parabola

then you can use calculus or algebra. simply completing the square should answer this for you without too much effort.