Irodov Problem 1.20

a)





b) At t=0, r=0 and thats the initial position of the particle. The equation r=0 has another solution besides t=0 and that is and this is when the particle will return to its initial position. The maximum distance that the particle travels is when v=0 at, . At this time the displacement of the particle is
.


Since the particle has to traveled the same distance to return to its initial position, the total distance traveled is .