The speed with which you perform each repetition within a set is largely dependent on your fitness goal (i.e., gain endurance, gain muscle mass, gain strength, gain power).  Why is this the case?  Because your fitness goal determines the intensity (i.e., % 1-RM) as well as how many repetitions you perform (i.e., 8-12 reps).  This, in turn, determines how fast or slow you should perform each repetition which will ultimately determine the duration of your set.  For example,  if your goal is to gain muscle mass, you should perform about 8 to 12 reps at a moderate speed so that your set lasts from about 30 to 40 seconds.  The duration of the set is often referred to as time under tension (TUT).
     It is recommended the eccentric movement (i.e., downward stroke) of each rep should take at least two to four seconds duration (depending on intensity level) while the concentric movement (i.e., upward stroke) of each rep should take at least one to two seconds duration (depending on intensity level).   For example, more time should be spent  lowering the dumbbell (the eccentric movement) during a bicep curl compared to raising it (the concentric movement).  
     The more repetitions that are expected to be performed, the faster the speed of movement to ensure muscle fatigue does not preempt your goal reps.  The less repetitions that are expected to be performed, the slower the speed of movement to ensure muscle fatigue occurs within your goal reps.  
     To summarize, here are the recommended parameters that should occur relative to your fitness goal:

• TRAINING FOR POWER:

1. Intensity:  30-45% 1-RM or 85-100% 1-RM
2. Reps:  More than 30 or less than 6
   
3. Rep Speed:  Fast or Slow
   
4. Set duration (TUT):  10 seconds to 1 minute
5. Rest duration:  1 to 5 minutes

• TRAINING FOR ENDURANCE:

1. Intensity:  50-67% 1-RM
2. Reps:  More than 12
   
3. Rep Speed:  Moderately fast
4. Set duration (TUT):  30 to 40 seconds
5. Rest duration:  Less than 30 seconds

• TRAINING FOR MUSCLE MASS:

1. Intensity:  67-80% 1-RM
2. Reps:  8 to 12 
   
3. Rep Speed:  Moderate
4. Set duration (TUT):  30 to 40 seconds
5. Rest duration:  30 seconds to 1.5 minutes

• TRAINING FOR STRENGTH:

1. Intensity:  80-85% 1-RM
2. Reps:  6 to 8 
   
3. Rep Speed:  Moderately slow
4. Set duration (TUT):  20 to 30 seconds
5. Rest duration:  2 to 5 minutes   
   

NOTE:  Since rep speed (i.e., moderately slow) is largely ambiguous, set duration (i.e., 20 to 30 seconds) is a much better means to gauge how fast or slow you are performing each rep for the particular training goal (i.e., training for strength).

       The American College of Sports Medicine (ACSM) guidelines for special populations may vary somewhat as more knowledge is obtained annually.  Special populations consist of people who may have the following conditions:  lower back pain; high blood pressure; heart disease; diabetes; asthma; coronary obstructive pulmonary disease; arthritis; high blood cholesterol; obesity; overweight; pregnant women; people with AIDS or cancer; osteoporosis; people with shoulder impingement; paraplegics and quadriplegics; multiple sclerosis; epilepsy; and cerebral palsy.  Cardiovascular, weight training and flexibility categories with their specific parameters of frequency (i.e., days per wk), intensity (i.e., % HRR and % 1-RM), duration (i.e., minutes), and types of exercise are provided.