Suppose I have a battery-powered toy car, and I am told to design an experiment which would allow me to determine the average speed of that toy car over, say, a meter, and to account for experimental uncertainty somehow.
I can think of a couple of ways to do this, but no matter which one I consider, it is not clear to me how to incorporate uncertainty. Here is one proposed method:
(1) Put car on floor next to, but 50 cm behind, a meter stick, and turn car on. Get digital stopwatch ready. When front of toy car reaches beginning of meter stick, turn on stopwatch. Turn off stopwatch when front of car reaches end of meter stick. Use distance traveled divided by time to calculate average speed.
Obviously, I could simply get out my calculator and type 100 / (stopwatch reading) and write down the number that I get. However, that does not seem right, for several reasons. The distance (100 cm) must be uncertain because I cannot be confident that the car actually traveled 100.000... cm. The time is also uncertain because it is a digital device, and all digital devices have associated uncertainties, independent of reaction time. It is also uncertain because I cannot be confident that I started and stopped the stopwatch at the moment the car reached the beginning/end of meter stick. I could (somehow) assign an uncertainty to both the distance and time and then use normal rules for assigning an uncertainty of a calculated result. But I cannot think of how to express the value of the uncertainty.
The other method I can think of involves repeating the experiment many times, and then calculating the numerical average and the associated standard deviation. Then, my final answer would be in the form: value +- standard deviation, but it's not clear to me how I would go about rounding wither value; and, rounding those values seem, to me, to be necessary.
How would you experimentally determine the average speed of a toy car using a meter stick and a digital stopwatch only, and incorporate uncertainty of distances, times, and the average speed?