At a given instant, the merry$-$go$-$round is rotating with an angular velocity $=13rpm,$ and it is slowing down at a rate of $0\mathrm{.}4ra\frac{d}{s^2}.$

When the child is $2\mathrm{.}5$ ft away from the spin axis, determine the time rate of change of the child's distance from the spin axis so that the

child experiences no transverse acceleration while moving along a radial line. $($Round the final answer to four decimal places.$)$

The time rate of change of the child's distance from the spin axis is

fus.