# Including uncertainties in kenematic equations

1. Sep 22, 2008

### omarsalem91

1. The problem statement, all variables and given/known data
So basically I'm supposed to calculate final velocity given time, displacement, and initial velocity. The only problem is that I'm supposed to find these results with uncertainties included. I know the how to do basic calculations with uncertainties I'm just confused when formula constants are involved. See below.

2. Relevant equations
The formula I'm using is S=(U+V/2)*T\
These are my values. .103(+/-.1)= (0+V/2)*1.14(+/-.2)

3. The attempt at a solution
After I had divided displacement by time I needed to get the 2 out from under there so I multiplied. Heres where I got confused- What do I do about the uncertainties? Do I multiply them by 2 as well?

2. Sep 22, 2008

### LowlyPion

When dealing with product and division uncertainty propagation I think you are using relative or percentage uncertainties, so the effect of a constant 2 with no uncertainty, should have no overall effect on the relative uncertainty of the result. (It should of course double the Absolute uncertainty.)

For your example the relative uncertainty of S is .1/.103 is 97% (was there a typo in your uncertainty?)
And the T uncertainty is .2/1.14 = 17.5% yielding a total of 97% + 17.5% + 0% (for your constant)
Hence then on your measured result of .206/1.14 = .18 ± 114.5% = .18 ± .21 which may be nonsensical since V must have been positive?

Edit:Other treatments of uncertainty propagation use the RSS of absolute uncertainties for addition and subtraction and RSS of Relative uncertainties for multiplication and division operations, when the measurement quantities are independent.

In this case the sq root of (.97)2 + (.175)2 yields 98.6%

Last edited: Sep 22, 2008
3. Sep 22, 2008

### omarsalem91

Thanks so much and yes there was a typo- it was .01/.103