A $400$V$,50$ Hz$,$ Y$-$connecting, three$-$phase and four$-$pole linear induction motor drives a vehicle with a slip of $4\%.$ The motor pole pitch is $50$ cm$.$ The parameters of its equivalent circuit shown are: Primary side: R$1=0\mathrm{.}1,$ X$1=0\mathrm{.}35$ Secondary side: R$!"=0\mathrm{.}4,$ X$!$#$ $"=0\mathrm{.}5$ Magnetizing reactance: Xm $=10$ Determine:

a$)$ Linear synchronous speed b$)$ Vehicle speed c$)$ Draw equivalent circuit with parameters d$)$ The input and load current e$)$ The input and output power f$)$ The output mechanical power and thrust$/$force $($Pf&w $=150$ W$)$ g$)$ Efficiency