P2.14 A rotating load is connected to a field-controlled DC electric motor through a gear system. The motor is assumed to be linear. A test results in the output load reaching a speed of 1 rad/s within 0.5 s when a constant 80 V is applied to the motor terminals. The output steady-state speed is 2.4 rad/s. Determine the transfer function θ(s)/Vf (s) of the motor, in rad/V. The inductance of the field may be assumed to be negligible.

Also, note that the application of 80 V to the motor terminals is a step input of 80 V in magnitude.