The current in a $80\mathrm{.}0-mH$ inductor changes with time as $i=3\mathrm{.}00t^2-5\mathrm{.}00t,$ where $i$ is in amperes and $t$ is in seconds.

$($a$)$ Find the magnitude of the induced emf at $t=1\mathrm{.}00s.$

$$ mV

$($b$)$ Find the magnitude of the induced emf at $t=4\mathrm{.}00s.$

$$ mV

$($c$)$ At what time is the emf zero?

$s$