From a couple of slides presented at one of my seminars:
For strength: The goal of strength training is to increase your muscles’ capacity to produce force. As such the repetition style that leads to the highest force output will be the most effective.
Force = mass x acceleration.
This led to the development of the principle of Compensatory Acceleration Training (CAT) initially popularized by Fred Hatfield in the 1980s.
Basically, this means that your intent should always to push as hard as humanly possible, trying to accelerate the load as much as you can. This intention lead to the highest level of motor unit activation and firing rate.
Now, depending on the load the bar might go up slowly or fast. The method is named after the result you get without applying maximum force to the bar against light to moderate load: the bar accelerates a lot more… basically you compensate the lack of load by a higher acceleration.
The intent to accelerate a submaximal weight as much as possible leads to strength gains up to 2x that of a slower repetition cadence/not having the intent to accelerate as much as possible.
(Ref: González-Badillo JJ, RodrĂguez-Rosell D, Sánchez-Medina L, Gorostiaga EM, Pareja-Blanco F. Maximal intended velocity training induces greater gains in bench press performance than deliberately slower half-velocity training. Eur J Sport Sci. 2014;14(8):772-81)
For strength: Now, there is a second school of thought that promotes a concept called « dynamic correspondence».
Dynamic correspondence refers to using the same movement dynamics as you would see during a maximal effort lift (or near-maximal effort).
So, if during a maximal or near-maximal effort, the concentric phase is completed in 2 seconds then even your lighter sets should have a 2 second concentric.
The logic is that your lighter weight sets become « practice » for limit strength work and you thus want to make it as similar from a timing/rhythm perspective.
This comes from weightlifting (olympic lifting) where, if you are doing a full snatch with a light weight and accelerate it as much as possible it will be lifted way too high to catch it in a full snatch.
The timing element in the competitive snatch, clean and jerk is also a lot more critical than in the strength lifts.
The same approach cannot be used effectively in the development of strength in the basic compound lifts as this type of rep style will lead to a much lower neuromuscular training effect and no benefit from a timing/technique perspective.