I am doing rebranding of a company that provides internet through fiber-optic cables.
I want to portray "FAST", "fiber optics" and "connectivity" in that logo. In all my initial sketches, I have catered the later two but not the first.
If you can provide link to your own or any other work which represents this then it will be highly helpful.
There are several ways you can represent "fast" in a logo. One way is to "italicize" the logo (text and/or graphics) which conveys movement. The more you angle the content, the more speed is implied. However, too much angling could distort your work.
Adding lines behind the movement might help. See GiantCowFilms example for this.
You might also consider only angling part of the logo, especially if it naturally fits that part of the logo. Italicizing words like "express" or "fast," if part of the company name would imply speed.
Another approach might be to add a slogan or other text that can imply (or outright state) that the company is fast.
Finally, you can find a symbol that gives the impression of the company being fast. Jets are a great approach but often do not fit the company's business. Think of other ways you could show "fast," even if they are not entirely realistic.
Attribution: The hand extending from the computer monitor design was downloaded from FreeVectorArt.net. It is being used under the Creative Commons Attribution 3.0 License. It was designed by Vector Open Stock.
I hope these ideas help.
Something like this should get you started. The key is to imply motion by making the text appear to be trying to go somewhere. and because we read from left to right, make go from left to right. Otherwise it will appear to be moving "backwards".
Note: the graphic is awful looking, but it is there to demonstrate a concept.