*If we changed our speed limit signs to metric, what would probably replace 55 m

Physics
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*If we changed our speed limit signs to metric, what would probably replace 55 miles/hr? Answer in m/s with the correct number of significant figures, and note that 1 mile  = 5280 feet and 1 inch = 2.54 cm.

Oct 3rd, 2015

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To convert 55 miles per hour into meters per second, we need to multiply 55 by a series of conversion factors.  First of all, we need to convert miles into meters.  1 mile=5280 feet, so we multiply 55 miles/hour by 5280 feet/mile to get 290400 miles*feet/hour*mile.  And since the miles in the numerator and denominator cancel out, that is the same as 290400 feet/hour.

We convert feet into inches the same way, multiplying 290400 feet/hour by 12 inches/foot.  After canceling out the feet in the numerator and denominator, we're left with 3484800 inches/hour.

Converting inches into centimeters, we multiply by 2.54 centimeters/inch, leaving us with 8851390 centimeters/hour.

Converting centimeters to meters, we multiply by 0.01 centimeters/meter, leaving us with 88513.9 meters/hour.

Finally, we convert hours into seconds.  We multiply by a conversion factor to cancel out the hours and leave us with seconds as before, but since the hours are in the denominator, we need hours in the numerator of our conversion factor, and seconds in the denominator.  Therefore, we multiply by 1/3600 hours/second (this is the same as dividing by 3600), leaving us with 24.5872 meters/second.  

We now need to round to the appropriate number of significant figures.  Since we are multiplying, the number of significant figures is equal to the smallest number of significant figures in the numbers we multiplied.  In this case, that is the two figures in 55 miles/hour.  Therefore, our final answer is rounding 24.5872 to two significant figures to leave us with 25 meters/second. 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 19th, 2015

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