A wneel, starting from rest, rotates with a constant angular acceleration of $3\mathrm{.}70ra\frac{d}{s^2}.$ During a certain $7\mathrm{.}00$ s interval, it turns through $142$ rad $.($a$)$ How long had the wheel been turning before the start of the $7\mathrm{.}00$ s interval? $($b$)$ What was the angular velocity of the wheel at the start of the $7\mathrm{.}00$ s interval?

$($a$)$ Number $$ Units $$

$($b$)$ Number $$ Units $$