Why take your time to speed up or down...

Slowing down...

 So when slowing down one must consider the simple fact that such a large amount of weight needs a bit of time to react to speed adjustments. Many efforts in design and maintenance are made to make sure the response time of the engine matches the load as quickly as possible - considering the laws of physics.
Others things to consider when slowing down; the Propulsion Electric Motor (PEM) are connected to main electrical system of the ship, which means that along with lights and propulsion, are connected computers and other sensitive electronic systems. These systems do not respond well to changes in frequency / voltage and that is why numerous safety devices exist.
When abruptly slowing down on the propulsion motor telegraphs, as if downshifting in a "sport car", the load on the PEM is rapidly reduced. This in turns reduces the load on the generator, which is sensed by the engine's governor, reducing the fuel needed to turn the engine at the steady RPM needed. Slight performance imperfection in any of the many components of the system may slow that response, and the result would be a governor delivering too much fuel for a load that is no longer there, therefore speeding up the engine.
This slight surge may be enough to activate the various safeties designed into the system such as over voltage, frequency fluctuations and reverse power. The reverse power safety system detects when other engine(s) are driven by the faster engine, which will trip the circuit breaker, this generally causes an overload on the remaining generators, tripping them as well, resulting in, of course, a total black out.
So the moral of this little story is "take your time slowing down", although the bridge is far removed from the sounds and feels of the propulsion system, please consider the mass of steel and iron that needs to adjust. Avoid the temptation of slowing rapidly from 140 shaft rpm to 0 in one fast swoop. Even in an emergency, take a "minute" and prevent a bigger problem, like a black out, and a possibility of frying anything electronic.

If a speed change can be planned, it is always best for operational needs to give the Engine Room a ten minutes advance warning. That time allows the engineer and motormen to adjust water production, or steam consumption to match the engine load, assuring a constant service to all steam users.    

Speeding Up...

Speeding up needs the same considerations as slowing down, although the results may not be as dramatic as a black out. A lack of care when speeding up could be very damaging to the company in government imposed fines and sanctions, due to excessive visible pollution. Not to mention the real worries, thermal load of the numerous engine components.
Much more time is required when speeding up to full speed on the PEM; in particular, the upper range of load. Generally, the engines will easily adjust to loads up to 50% therefore usually not an issue during a "Stand By" condition. The problem of overloading the engines usually arises after "Stand By", where people just want to "get on with it!" when in fact its the most critical time for loading the engines.
There is no real rule of thumb of how many minutes it takes to reach full load in a safe and considerate manner, but the telegraph operator should expect 1/2 hour after "Stand By", before safely reaching full load on the engines.
The best guide for the average person is smoke from the stack. Anytime smoke is visible, it is an indication of overload, because fuel is not being burnt properly for whatever reason; "cold steel", reaction time of temperature devices, speed of turbo-charger, etc. If speeding up and a thick black smoke is noticed from the stack, the step taken was too much, reduce a little and wait until the smoke is not visible in order to take the next step.
Remember that the anxiousness to get up to full speed is usually the highness, when you need to take the most time speeding up, towards the 80-90% load on the engines. In this power range, a 5 shaft rpm increase may take 10 minutes to achieve without overloading the engines. 

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