Measuring Speed Decay - Calculating Time to Stop

[phutoo]

Hi, I was wondering how I would find the speed decay of a ball rolling in a straight line, if i were to measure the time it takes to travel a certain distance over and over. i.e

[FONT="Courier New"]
>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>>
<---10cm--> <---10cm--> <---10cm-->
           ^           ^           ^
      record time  record time  record time

So then with those 3 time measurements (or less), could the time be calculated for when the ball will stop? This is just a question I've been thinking about for a couple of days and I just can't figure it out :)

 

[rcgldr]

You'd end up with 4 samples of position versus time to work with. You could then use this information to do a curve fit, perhaps a polynomial, or you could assume some specific equation type and do an exact fit.

 

[sophiecentaur]

If the ball happens to be going fairly quickly, a TV movie could show you the separate images of the ball at successive 1/60th second intervals (or whatever frame rate you happen to be using.)
Failing that, a stroboscope with, say 1/10s flashes and a camera set to long exposure (dark room, of course) could also give you a set of sharp images on the same picture. Do the whole thing in front of a metre rule and all the info (times and distances) is there on the picture for you

 

[phutoo]

Yes but the problem is I want to be able to calculate the distance it will travel just from a few measurements at the beginning.

I'm not too sure about what you said rcgldr; how would I fill in the rest of the curve?

I was thinking from the first time measurement, I would have time and distance, so I could calculate the speed at that point to be dist / time. But then how could I calculate the de-celeration? or am I going about this all wrong? :)