Let's say the Earth suddenly and jarringly accelerates to the point where day becomes night in a few seconds (assuming it was originally noon at the point of observation and that equal time was taken to accelerate and decelerate). What kind of undoubtedly apocalyptic effects would this have?
XKCD calculated what would happen if you spun up the Earth to have a 1 second day. Short answer, the Earth would spin into a flat disk, flinging out matter at a decent fraction of the speed of light. Within seconds, everyone would be dead, and the expanding rock would crash into satellites and the Moon with such speed that they would release huge amounts of gamma rays. The rock would spread through the solar system within a couple days. It is unlikely much (possibly even the Moon) would be hit because of how the Earth is tilted relative to everything else, but anything it does hit would end catastrophically.
The Earth would probably spin apart.
Normally, standing on the equator, you're moving at the relatively slow pace of 1 earth circumference per 24 hours. Your momentum would carry you straight off into space, tangent to the surface of the Earth, except gravity keeps pulling you down. It does this far more strongly than you need to stay on the surface. Using a web site to let me calculate the orbital velocity around the Earth, with a height of 0m, I calculated that a trip around the Earth would take 84.48154038573982 minutes. This means that if Earth spun that fast, you would have just enough gravitational attraction to keep you on the surface.
You're asking about MUCH faster. Even if the Earth slows down afterward (which I think you're suggesting with 'decelerate'), the speed at which that rotation occurred would fling huge pieces of the Earth into space. I don't have any hard numbers (maybe try the Physics SE for that), but I have no doubt that the centripetal force required to keep the planet intact would far exceed the force of gravity and the chemical bonds between parts of the Earth. You might see a few large chunks of tectonic plates stick together as they fly off into space, but I suspect even those wouldn't fare well.
Given this, one has to ask what exactly is causing this speedup. If it's some massive adamantium rod running through the planet, being turned by some being of godlike power, the rod would probably just rip through the Earth. Dealing with forces that powerful, the Earth's crust would have about as much chance of holding together as water or air. If the planet is just magically sped up, every single molecule, it will fly apart.
Now, just for argument's sake, you did mention 'decelerate', so maybe the same unbelievably powerful force spinning the Earth is also holding it together while spinning it, until it stops and lets it go back to normal. Then it's a question of how that force was applied. If it somehow made all of the planet, but no man-made buildings, move, then they'd have no chance at holding on. Most buildings would have the ground yanked out from under them so quickly they'd stay mostly intact, like glasses on a tablecloth that's pulled out, until something at a slightly high elevation spins into them. That mountain over there? It just went through your house. "Now", you may say, "I built my house on top of Mount Everest just in case that happened!" Well, I hope for your sake that whatever is 12 hours rotation around the Earth from there is the same height, because now that the Earth has stopped below you, your house is falling for whatever the difference is. In short, anything that isn't magically accelerated and held together with the Earth is debris.