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The operating region of the developed torque 
and speed (
) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque 
characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortest time?
The shortest time to reach the final operating point S happens when the motor accelerates with the maximum possible torque.
In the given 
characteristics, the maximum developed torque corresponds to the uppermost boundary of the shaded region, the line 
.
So, the fastest trajectory will follow: .
Hence, correct answer is option (a).