2. Imagine that you are driving down a stretch of freeway with a posted speed li

Question

2. 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.

Explanation / Answer

for example : you measured a long stick and it was 50cm, but you were suspicious if it was 50.00000000 cm so it might be 49.998 so your uncertainty is -+ 0.002cm

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