As an example let us consider someone in the bottom position of a benchpress.
At time t=0 he starts pressing the barbell upwards and at time t=tl he locks out the press.
While pressing he excerts a force upwards on the barbell: F.
Gravity on the other hand exerts a force downward on the barbell: mg, where m is the mass of the barbell and g=9.81 m/s^2.
The net force on the barbell is:
F-mg>=0
According to Newtons 2 law:
F-mg=ma
<=>
a = F/m - g

So the force the lifter excerts on the bar causes the speed of the bar.
Unfortunately the force output of a muscle decreases monotonically with velocity:

Trought the lift the velocity increases until the force drops down to mg at which time the acceleration is 0 and the bar has reached its maximum velocity. This velocity can be found by taking the intersection between the force velocity curve and a horizontal line where F=mg.
Training at low velocities lifts the curve at low velocities but does little for the curve at higher velocities.
The solution is to train over a range of velocities so that you can produce as much force as possible at every velocity you are interested in.
For instance instead of only deadlifting 110 kg for grinding/slow reps you may alternate this with deadlifting 80-90 kgs for explosive/fast reps or powercleans at say 60 kg. In both cases your power production will be larger than with the grinding/slow reps.
Here are some more examples of exercises that works on different parts of the force velocity curve:
