$12\mathrm{.}13$ A vehicle is powered by a linear induction motor with a pole pitch of $2$ m $.$ The primary circuit resistance $R_1$ is $0\mathrm{.}5,$ and the secondary resistance referred to the primary circuit $R_2^{\text{'}}$ is $1\mathrm{.}0.$ The equivalent inductance of the primary plus secondary circuits is $0\mathrm{.}02$ H $.$ The frequency of the primary windings is $10$ Hz $.$ Assume that the drag force is $500$ N and the friction force is $2$ kN $.$ Compute the voltage across the primary windings when the motor travels at $100k\frac{m}{h}.$