In order to answer your question, we need to consider a number of concepts. The first is the force-velocity curve which, in the most simple terms, is a plot of the relationship between the force and speed of contraction. As contractile force goes up, contractile speed goes down, and the relationship is curvilinear.
This phenomenon is the consequence of motor unit recruitment and the size principle—"...motor units are recruited in a precise order according to the magnitude of their force output, with small units being recruited first, thus exhibiting task-appropriate recruitment" (emphasis added)—and the size of the load relative to an athlete's absolute strength. If the athlete lifts a one repetition maximum, they recruit all of their available motor units, and their peak force output is very close to the minimum amount required to accelerate the load. (Think F=ma.) At this end of the range, the resultant velocity is a function of force production and strength endurance; the athlete needs to produce enough force to get the load moving, but must also move the load quickly enough so as not to fatigue. At the other extreme, small motor units can easily meet and exceed the force requirements, and the load has insufficient inertia to provide resistance to movement that would allow larger motor units to be recruited; that is, the load moves before the larger units can be recruited.
It is common in the field of performance training to suggest that we can find the ideal power training load by superimposing a force-velocity curve on a power-velocity curve, as illustrated here
The cyan coloured line, in this figure located at about 40% of the one repetition maximum, represents the proposed ideal load, since that is where the greatest power is achieved. However, this fails to account for the differences in activity, and indeed our definitions of power.
Formally, power is the time-rate of energy transfer. And since energy is a function of velocity, power does indeed determine acceleration. However, this simplistic view of power fails to account for what we know about the mechanics of motor units. Motor unit development is highly specific to the activity being performed: the kind of power that Aroldis Chapman requires to pitch a fastball is very different from that Hafþór Björnsson requires to throw a 90-pound sandbag over 15-foot-high bar. In the former case, the projectile represents a small part of the load; the velocity at which the ball is pitched depends upon the speed at which relatively small motor units can be recruited to overcome the inertia of the arm complex and ball combination. In the latter case, the projectile represents the bulk of the load, and the height to which the sandbag is cast depends upon larger motor units.
Thus, distinct types of power have been identified, originally described by Bompa in his masterwork Periodization: Theory and Methodology of Training. Variations on these classifications exist, but the principle remains the same: power is specific to the activity, and thus power training must also be specific. Furthermore, as described by Bryan Mann in this excellent article, analysis of an individual athlete's load-velocity profile can help us identify the factors that are limiting power output. "By examining the slopes of these curves, we can see if individuals are more deficient in velocity or force." In such cases that force is deficient, slow lifting may initially improve power. This explains the observation found by research studies, which tend to use novices.
However, more generally, power should be developed with a load that is specific to—that is, not deviating too far from—the load characteristics of the discipline. Striking speed for a football might best be developed with a load of a few kilograms attached to an ankle weight or cable; a sprinter's starting speed might be developed with a moderately loaded (30-40% of 1RM) jump squat or broad jump; a weightlifters clean would be developed with a heavily loaded deep squat. In every case, assuming that the athlete has adequate technical mastery, the exercise must be performed ballistically. This is critical both to produce the right force characteristics (remember that force is a function of acceleration) and to develop explosively powerful motor units.
I hope that is helpful.