Variable acceleration/velocity of an arm in motion

[matb]

I'm a karate instructor desperately trying to find a model or formula that explains what happens to the to speed and acceleration of a limb under varying conditions.

If you assume that a limb has a travel distance of 3 feet, moving from stationary, and the limb weighs 5 kilos.

If I assume that it takes .2 econds for the limb to travel its total distance, yet achieves maximum acceleration after 1 foot, does the remaining travel time at uniform velocity slow down the overall acceleration from what it was at 1 foot, or does that figure remain the same?

What if I assume a constant increase in acceleration for the entire .2 seconds - how does that change the other variables?


What formula do I use to prove it?

 

[Danger]

I haven't a clue, but it might be productive to combine this with Physicsfan's question about pitching speed. It seems as if it's the same problem in a different context.

 

[rcgldr]

I've done a bit of martial arts, but have much more experience with table tennis. It's been my experience as well as experts that the more distance your arm moves before contact with the ball, the faster the blade speed, at least in the case of a swinging arm type motion. This implies that acceleration continues for more than just one foot of travel, in the case of a loop shot where your arm is used similar to a golf club, except you snap your elbow and wrist just before contact for even more blade speed.

Similarly, boxers punches are stronger when the distance the arm has moved before contact is greater.

However, in both these cases, you're moving a bit of weight held or attached to the hand.

With no weight on the hand, I don't know if there's a maximum near no-load velocity a person can generate due to muscle limitations, but again, in my observations during breaking demonstations, more distance generally translated into more speed and therefore more energy.

So it's my opinion, that a persons arm continues to accelerate (but at varying amounts) until contact or reversal of muscle inputs (or you reach the limits of a joint).

A high speed video or film could capture movements, and then analyzed to generate actual numbers. This has probably been done, but I haven't found any links to provide here.

 

[matb]

A table tennis stroke is a swing, and there is a delay in transmission of hip motion to arm motion in that instance. Furthermore, there is a body weight component that enables you to transmit force through the joints to the arm.

TBH, rather than a debate on whether or not the arm continues to accelerate throughout its entire duration, I was looking for the simple maths that makes the comparison between short acceleration and long uniform speed travel, and uniform acceleration over the entire duration of the strike.

Thanks for your input.