Question $8[8]$

A $3$ kg disk slides on a smooth horizontal table and is connected to an elastic cord with elasticity constant $\backslash ($ k$=15\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The cord is initially unstretched and has length $\backslash ($ r$=0\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash ).$ The disk is then given an initial velocity of $\backslash (5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ in the transverse direction.

$($a$)$ What is the transverse velocity of the disk when the cord is stretched $0\mathrm{.}3$ m $?$

$($b$)$ At what rate is the cord streched at that instant?