Problem 1.105

A particle of mass $m$ moves in a certain plane $P$ due to a force $F$ whose magnitude is constant and whose vector rotates in that plane with a constant angular velocity $\omega .$ Assuming the particle to be stationary at the moment $t=0,$ find: (a) its velocity as a function of time; (b) the distance covered by the particle between two successive stops, and the mean velocity over this time.