Peg A moves along a curved fixed channel

whose shape is described by $r=b+c*cos.$

The peg is driven around the channel by the

slot in member $OB.$

a$)$ Write the equation for the position vector

$r$ of A using cylindrical coordinates.

b$)$ Use your answer to a$)$ to write the

equations for the velocity $v$ and

acceleration a vectors of A using

cylindrical coordinates.

c$)$ Calculate the magnitude and direction of

$v$ and a for these conditions: $b=3\mathrm{.}00cm,$

$c=2\mathrm{.}00cm,=\frac{}{2}$rad,${}^{}=5\mathrm{.}00ra\frac{d}{s}$

counterclockwise and ${}^{}=20ra\frac{d}{s^2}$

clockwise.