: Doctor Joel Seedman and PulseSpeed training If speed is dependant on force as Newton's first law of motion suggests then shouldn't training with no weights by moving limbs at really high speed be as effective as moving heavy

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I think you mean Newton's second law. First law is an object will remain at rest until acted upon by a force.
Yes, using force=mass* acceleration, you can build on acceleration vs mass in order to increase force. The force output is noticeably different based on the larger of the ratio of mass and acceleration despite the output being the same.
Let me explain using with weights and without..
Even when we try and move as fast as possible with heavy weights, we still move the weight slowly.
Lifting heavy weights forces you to move slowly.
This slow, but still maximal speed is key for producing adaptations that lead to improved maximal strength, because "); it simultaneously recruits all motor units while also allowing a maximal number of actin-myosin bindings inside the individual muscle fibers.
We can partially replicate this situation inside the muscle by using lighter weights while training to muscular failure. This also produces full motor unit recruitment while simultaneously creating a maximal number of actin-myosin bindings inside individual muscle fibers.
However, the effect is not identical, because lifting a light weight to failure involves a lot of fatigue, and this means that many of the motor units are not actually producing very much force by the time full motor unit recruitment is reached.
the law works.. You could try to increase your speed by doing speed trsining, such as sprinting or lifting heavy weights(60% of 1RM) but doing it as fast as you can, or work on explosive movements. The speed will plug itself into the acceleration portion of the following equation:
Force=mass*acceleration
And it will produce greater force.
Lifting weights quickly involves a much larger neural stimulus but a much smaller tension on each muscle fiber compared to lifting heavy weights, and this produces totally different adaptations. You're building high velocity strength vs low velocity strength, and focusing more on single contractile movements. The body's type 1 fibers are also trained pretty heavily over type 2 fibers which results in more endurance. Jackie chan weight trains with relatively light weight and does 25 to 30 reps as fast as he can, and he is very strong, but in a different way than a guy picking up a 300 lb stone is strong. Jackie chan can vault over buildings and swing his body around like it's a feather, while the strong guy picking up 300lb can't, Jackie chan probably can't haul a 300lb stone.
Training with purely bodyweight would emphasize the high velocity aspect, but your body needs to become stronger in order to move faster. The less weight you use, the faster your body has to move Your muscles have a limit on how fast they can move, especially if you're not strong to say.. do a pushup. Think of a linear scale, where the heavier the weight it, the less speed you have, and the lighter the weight, the more speed. Near the beginning of a scale, with 0 weight(think a bicep curl), you can only curl your arm so fast. However, there is a sweet spot of picking a light weight and doing very fast movements, which would be more beneficial than doing really fast push-ups, you can do Jackie Chan's bench press move with 135lbs as fast as you can for 25 reps, etc..
You could graph a series of equations based on various numbers of your different weight lifting movements, and use the lines given in order to see the speed necessary. A time complexity variable for speed would make this a 3d chart that you could use to find the optimal strength per possible given the lightest weight.