$[$C$]$ A solid sphere of radius $5\mathrm{.}00[cm]$ and mass $200[$g$]$ is set moving on a level surface with initial velocity $1\mathrm{.}2[\frac{m}{s}]$ and a backspin of $w=-6[ra\frac{d}{s}].$ The coefficient of kinetic friction is $m_2=0\mathrm{.}15.$

Set up Newton's second law for both linear and rotational motion. $[6$ points$]$

Set up the equations for the velocity and angular velocity as functions of time. $[4$ points$]$

Calculate the linear velocity and the angular velocity at the time they first satisfy $v=r.[8$ points$]\{$hint: eliminate $f\frac{t}{m}$ from the equations.$\}$

Calculate the time at which $v=r.[4$ points$]$