You need to know the full load torque curve of the motor over its speed range, and the rotational inertia of the total motor and driven equipment, and the build up of load over the speed range, if any. The result is the acceleration curve over the speed range, which will give you revs per sec. up to full speed and hence the time.
Also very necessary for working out the time to overspeed the motor/engine up to failure speed if there is a complete breakaway of the load, and the response time needed in the design of an automatic shut off system of the imput power/fuel before machine failure. Imperative if you are designing shut down systems for nuclear power station emergency power generator sets as that is the last thing you need to fail - apart from the coolant pumps themselves!!!
Acceleration time t is given by t=(GDsqχS)/(375χTa)
where GD sq is the total gd sq of motor+Driven equipment GDsq in KG Msq+gd sq of fly wheel etc
s is speed in rpm and Ta is average acceleration torque.Average acceleration torque is to be computed by plotting T_S Curve of Motor and superimposing driven equipment T_s curve on that and area below the two curves gives acceleration torque.Now a days softwares are available which can do the job faster.
__________________
To avoid crticism do nothing,say nothing,be nothing