The sports training principle known as S.A.I.D. or Specific Adaptations to Imposed Demands means that your muscles, tendons, and nervous system will grow and develop based upon the way you exercise them. In other words, if you train by lifting weights very slowly, you will not do much to improve actions that require you to move quickly, such as, golf, tennis, basketball, or martial arts. In fact, running for endurance causes the body to adapt by making fast twitch muscle fibers change into slow twitch ones. Therefore, training slowly may prevent you from moving as fast as you could before the training; if your desired activity requires speed or quickness, you must train for speed and quickness.
Heavy squats will build great lower body strength; however, you will not necessarily see your vertical jump height increase proportional to the increase in your squatting weight. To improve your jumping height, practice pylometic jumping drills. Even though your arms move similarly to a punch when you are performing a bench press, heavy bench pressing will not make you punch much harder or faster unless you also practicing punching drills. Since martial arts require twisting and moving in more than one plane of action, you need to train with twisting in all three planes of movement. Multi-planar exercises are more complex and more difficult to perform properly so most people need to be taught how to perform these exercises correctly. One plus is that they usually require less equipment.
Heavy slow lifting may be great for hypertrophy (making muscles grow); however, it will not help to give you the explosive power you need for the martial arts. In fact, training for strength in a manner in which you are not going to use the strength can be detrimental because you may develop more strength than your body can safely control. This is one reason why athletes are always injuring their hamstrings. They train to go forward or up, but they do not train to decelerate or stop.
In the past, warriors trained to fight by fighting. One may increase are strength by swinging a sword faster. Acceleration requires force. Greater acceleration requires greater force. Therefore, by swinging a weapon faster, the muscles the warrior used to swing the weapon became stronger, even though the weight of the weapon did not increase. To punch or kick faster and stronger, practice punching and kicking faster and faster for many, many repetitions. Muscles can only contract from their attachment points towards the center; they do not contract toward either side. S.A.I.D. works because, although muscles can only do one thing—contract—there are other factors that help determine what the final result of a given muscle’s contraction will be:
Speed of contraction. Strength of assisting, stabilizing and opposing muscles. Length, range of motion and elasticity of assisting, stabilizing, and opposing muscles. Core stability. Stability of our legs. Ability of all of the muscles involved to fire in the proper sequence and with the proper force for the proper length of time Confidence in our ability not to get hurt by being able to stop or reverse the action at the proper time.
In conclusion, to improve the strength and quickness of your punches and kicks, perform the individual punches and kicks faster and faster for many, many repetitions every day. Cross-training may help prevent training boredom and even be a relaxing moment, but it will do little to improve the skills that you need in your martial art.