Newton's second law, adapted to rotation: Accelerating Torque = Inertia * Angular Acceleration
The overall formula commonly used (in SI units) is:
ta = Wk2 * Delta N / 308 * Ta
Where
ta acceleration time (seconds);
Wk2 total connected inertia (lb * ft2);
Delta N speed change during time ta (rev/min);
Ta average accelerating torque (lb * ft) (average motor torque – average load torque)
The tricky part, as Bill mentioned, is getting the inertia and load torque curve data. You can get it fairly easy for the motor itself, usually the mechanical transmission components too, but getting it for the actual load can be challenging. For some machines, such as centrifugal pumps and fans, inertia at start-up is only the components themselves and the average load torque is usually something the pump manufacturer can provide because they needed that in order to select the pump. For a machine tool, it's also often fairly easy to attain this because it's consistent (as long as the tool is started unloaded). For a conveyor, hoist, or other material handling application it's going to depend on actual loading on the conveyor, which may vary greatly. Typically this would be calculated based on a "worst case scenario", for example after a power failure where the conveyor was fully loaded and dead still on re-start.
"You measure the size of the accomplishment by the obstacles you had to overcome to reach your goals" -- Booker T. Washington