In a $2-$pole, three$-$phase PMAC drive, the torque constant $k_T$ and the voltage constant $k_E$ are $0\mathrm{.}5$ in MKS units. The synchronous inductance is $15$ mH $($neglect the winding resistance$).$ The PMAC motor is driving a purely inertial load. A constant torque of $5$ Nm is developed to bring the system from rest to a speed of $5,000rpm$ in $5$ s $.$ Neglect the stator resistance and the leakage inductance. Determine and plot the voltage $v_a(t)$ and the current $i_a(t)$ as functions of time during this $5-$second interval.