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[/FONT]

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? :)

 

[PJC01]

Hello,

Thank you for your question. To find the speed decay of a ball rolling in a straight line, you can use the formula for deceleration:

Deceleration = (Final Velocity - Initial Velocity) / Time

In this case, the initial velocity is the speed at which the ball is rolling, and the final velocity is 0, since the ball will eventually come to a stop. The time can be calculated by taking the average of the three time measurements that you have recorded.

Once you have the deceleration, you can use it to calculate the time it will take for the ball to stop completely using the formula:

Time to Stop = Initial Velocity / Deceleration

I hope this helps answer your question. Let me know if you have any further questions or need clarification.

Best,