A particle moves on a straight line, \(\mathbf{r}=t \mathbf{u}\), from the center of a disk. If the disk is rotating with angular velocity \(\omega\), then \(\mathbf{u}\) rotates. Let \(\mathbf{u}=\) \((\cos \omega t) \mathbf{i}+(\sin \omega t) \mathbf{j}\)

a. Determine the velocity, \(\mathbf{v}\).

b. Determine the acceleration, a.

c. Describe the resulting acceleration terms identifying the centripetal acceleration and Coriolis acceleration.