If a ball is given a push so that it has an initial velocity of $7\frac{m}{s}$ down a certain inclined plane, then the distance is has rolled after $t$ seconds is piven by the following equation.

$s(t)=7t+4t^2$

$($a$)$ Find the velocity $($in $\frac{m}{s})$ after $2$ seconds.

$\frac{m}{s}$

$($b$)$ How long $($in seconds$)$ does it take for the velocity to reach $35\frac{m}{s}?($Round your answer to two decimal places.$)$

$5$