Mechanical time constant of PMDC Motor in starting and after switching off the supply is same or different?
Is that loop what you really have, or are you connecting a low impedance supply across the motor on startup, but open circuiting the motor on switch off? 

These conditions are not the same. Switch a short circuit across the motor on switch off and watch the thing comes to a screeching halt (All the K.E. will end up as heat in the motor windings).