If a rock is thrown vertically upward from the surface of Mars with velocity of $20\frac{m}{s},$ its height $($in meters$)$ after $t$ seconds is $h=20t-1\mathrm{.}86t^2.$

$($a$)$ What is the velocity $($in $\frac{m}{s})$ of the rock after $3$ s $?$

$\frac{m}{s}$

$($b$)$ What is the velocity $($in $\frac{m}{s})$ of the rock when its height is $10$ m on its way up$?$ On its way down? $($Round your answers to two decimal places.$)$

up $$

$\frac{m}{s}$

down $\frac{m}{s}$