Question on 1 problem graphical determinations

[terpsgirl]

Question on 1 problem...graphical determinations

1) Why is a graphical determination of the avg velocity obtained from the slope of a best-fit line drawn for the data more accurate than simply dividing the total distance by the total time?

It isn't.


Why is this? I said it was more accurate...why isn't it?

 

[JohnDubYa]

The average velocity (I think you meant speed) is defined as the total distance traveled divided by the total time of travel.

Essentially the maximum precision of any calculation is determined purely by the precision of your data. So the most precise determinations of results will always come straight from measurement.

To maximize the precision, you need to maximize the size of the measurement. (It is easier to measure the width of a table to a given relative precision than a grain of sand.) The total distance traveled and the total time of travel are the largest measurements you have, so the most precise results will be obtained from these two values. Any other method will always introduce some amount of random and systematic error, such as the inability of humans to draw accurately.

 

[maverick280857]

So the more data you have (the more measurements) the greater the chance of minimizing the error on average (as you can easily see yourself without major mathematical computations--supposing n values each have an error ei so the can be written as (actual)+/-(error). The mean of these n values is simply (1/n)*(summation of actual values) + (1/n)(summation of errors with signs). Clearly the error sum tends to a very small quantity as the number of terms increases. This isn't a rigourous proof but a heuristic one that should see you through.)

Hope that helps.

Cheers
Vivek