Originally Posted by **ChipB** If you have a formula like this for distance as a function of time (I assume here that your variable 'x' is time, and f(x) is distance), then velocity is simply the first derivative of the distance function with respect to time and acceleration is the second derivative. This gives you a good approximation of velocity and acceleration as function of time. The max velocity occurs either when acceleration = 0, or if acceleration doesn't equal zero at any point then either at the beginning or end of the run. If you find several values of time where acceleration = 0 then the next step is to take the derivative of the acceleration function and see if that value is negative at the point where acceleration = 0; if it's negative then you have a local max for velocity. As for how to create a rating system - that's a subjective question, as you first need te determine the relative "worth" of top speed versus top acceleration versus best overball time. One way to do it is to divide the slower runner's top velocity and divide by the faster runner's, and exprss it as a percentage. |

I see. I think the graph program I mentioned has a derivitive function built in. I tried it out and it is actually pretty darn close to what I estimated using the 5-yard segments. However, when I then took the derivitive of the velocity v. time equation, I got a peak acceleration of only 0.5 yards per second-squared. Not sure if I did it correctly or not.

You may remember, Chip, that you also helped me with a similar problem a while back regarding sprinters over the course of 40 yards with only 4 data points. Your help, once again, is much appreciated.