Uncertainty Help: Solving Homework on Speedometer & Measured Speed

[david2009]

Homework Statement

Imagine that you are driving down a stretch of freeway with a posted speed limit of 65 miles per hour. You aren’t sure whether to trust your speedometer, so you check your speed against a series of distance markers along the interstate. You notice that, in the time it takes you to count to ten, you pass the 0.2 mile mark. Your speedometer, marked in intervals of 5 mph, reads 65 mph.
a. Are your speedometer and your measured speed the same to within the uncertainty of your measurements? Assume a ±0.5 s uncertainty in your count; the mile markers have a 1% uncertainty in their position. Also recall the difference between standard deviation and uncertainty in the mean. [Note: DO NOT DO THIS ANALYSIS WHILE DRIVING!] Show all of your work.
b. You have just propagated the uncertainty in your ten second count through a series of calculations that involved multiplication and then subtraction. (If this wasn’t what you did, check your work!) You did this to test a hypothesis: that the speedometer reading was equal to your measured speed. Describe another, different situation where you might need to propagate the uncertainty through a series of simple calculations to test a hypothesis.
c. Let’s say that your uncertainty in your 10-second count was ±1%. Would you be able to tell that you were speeding? Show your work clearly and interpret your results.
d. Let’s say that your uncertainty in your 10-second count was ±1 second. Would you be able to tell whether you were speeding? Show your work clearly and interpret your results.

Homework Equations

The Attempt at a Solution

i tried todo the propagating uncertainty by applying substracting and multiplying to solve this proplem. but i stuck...
i found the uncertainty for a is 0.353 in my count.

 

[jbsteele]

a. Are your speedometer and your measured speed the same to within the uncertainty of your measurements? Assume a ±0.5 s uncertainty in your count; the mile markers have a 1% uncertainty in their position. Also recall the difference between standard deviation and uncertainty in the mean. [Note: DO NOT DO THIS ANALYSIS WHILE DRIVING!] Show all of your work.Measured speed = (distance/time) = (0.2 mile / 10 s) = 0.02 mile/s = 65 mphUncertainty in the count = ± 0.5 s Uncertainty in the distance = ± 1% = 0.002 mileTotal uncertainty in the measured speed = √(0.5^2 + 0.002^2) = 0.353 mphTherefore, the measured speed is 65 mph ± 0.353 mph which is equal to the speedometer reading of 65 mph ± 0.5 mph, so they are the same to within the uncertainty of the measurements. b. You have just propagated the uncertainty in your ten second count through a series of calculations that involved multiplication and then subtraction. (If this wasn’t what you did, check your work!) You did this to test a hypothesis: that the speedometer reading was equal to your measured speed. Describe another, different situation where you might need to propagate the uncertainty through a series of simple calculations to test a hypothesis.Another situation where one might need to propagate the uncertainty through a series of simple calculations to test a hypothesis is when calculating the acceleration of an object. For example, if you measure the position of an object at two different times and want to calculate its acceleration, you would use the equation a = (v2-v1)/(t2-t1). In this case, you would need to propagate the uncertainty in the position and time measurements through the equation in order to determine the uncertainty in the calculated acceleration.