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The above answer would be accurate if you are asking about a "back spin side kick."
If you are asking about a "back kick" (dwi chagi) also known as a "mule kick" then there is no need to pivot or turn 180 degrees.
With your target being directly behind you, simply lift the knee to your chest as you lean slightly forward, away from the target, and extend your leg rapidly to the rear. Your back remains to the target as you look over the shoulder of the kicking leg. The heel of the foot makes contact with your toes pointing down to the floor, or only slightly to the side. This could be directed to the opponent's knee, groin, abdomen, or solar plexus. This kick CAN also be done when turning backwards like a spin side kick, but the leg must travel directly under the torso, and do NOT rotate the hip fully around. The toes remain pointing downward as your back is more to the target for a back kick than the sideways position of a side kick.
You need to make your muscles stronger in your legs and abdomen. For your legs, you should do explosive drills, such as squatting and jumping. Having a strong core is really important as well. In order to kick faster, you need to have balance; a stronger core will help you do that.