Question about uncertainties in slopes of cars

[MrThelolking]

Hi,
I don´t know how this standard type uncertainty calculation can be solved. The situation is as follows: on a graph are three curves with different values, their slope is the speed of each car. The uncertainty of the y-axis (time) is 5%. Now the problem is that i want to display the values of the speeds in a table and as such a "universal" uncertainty should be given on top. I calculated the uncertainty of the fastest of the three cars to be +-0.3 m/s, the slowest car speed (ie slope) has a uncertainty of 0.5m/s. What value should I give for the universal uncertainty? Is it the average of the fastest and slowest? I feel somehow that it cannot be, as the average would be 40%, which would not agree with either of the values..
I did not find a similar problem in the internet (only one curve..), if you got any page of help, please redirect.
Thank you!

 

[rcgldr]

I'd swap the graph so that the horizontal axis was time and the vertical axis was position. Then the slope of a curve on this graph would be the velocity, except for the 5% uncertainty on the time axis. It would be easier if the cars started at time 0, position 0, so that the origin of the graph corresponded to the initial state of the cars.

I'm not sure what you mean by uncertainty. For any point on a curve, is the maximum error in the time value +/- 2.5% or +/- 5%?

If the speed of the cars is not constant, and maximum amount of acceleration is large, then it would be difficult to distinguish between a large amount of acceleration or an error between two sucessive sample points on a curve.

 

[Dale]

What you are describing is called "Propagation of Errors" where errors in some measured quantity propagate through some calculation to result in errors in the calculated quantity. This page has a good overview of errors, particularly the last section dealing specifically with the propagation of errors:
http://teacher.nsrl.rochester.edu/phy_labs/AppendixB/AppendixB.html

The table at the end of the last section includes a specific formula for the propagation of independent errors through a division. According to that formula, if you have a 5% error in time and a 0% error in the distance then you will have a 5% error in the velocity. If you observe a 5% error in time and a 40% error in velocity then there must be some error in the distance also or some correlation between time and distance errors.