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.