Average speed
- Thread starter gorond
- Start date
miles per hour is miles divided by hours not miles times hours.
HallsofIvy
Elite Member
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- Jan 27, 2012
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Can I have it without the fries?
- Joined
- Feb 4, 2004
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I accidentally discovered that a very useful technique (for me, at least) for this type of exercise is what engineers call "unit analysis" and what I call "cancelling units". The general process has you take the units you've got, the units they want, and all helpful conversion factors (such as "60 minutes per 1 hour", or "(60 min)/(1 hr)"), and set things up as one long multiplication. The trick is to make sure that the multiplication is set up so all of the unwanted units cancel off.
For instance, if one wanted to convert "20 miles per hour" to "(some number of) feet per second", one would need:
. . . . .5280 feet per 1 mile
. . . . .60 minutes per 1 hour
. . . . .60 seconds per 1 minute
Then one would set up the cancellation process like so:
. . . . .\(\displaystyle \displaystyle{\frac{20\, \mbox{mi}}{1\, \mbox{hr}}\, \dot\, \frac{1\, \mbox{hr}}{60\, \mbox{min}}\, \dot\, \frac{1\, \mbox{min}}{60\, \mbox{sec}}\, \dot\, \frac{5280\, \mbox{ft}}{1\, \mbox{mi}}}\)
How did I decide which values in each conversion factor went on top and which went underneath? By noting what I needed to have cancel off. If you're not sure, do the cancellation of the units to make sure that you're left with a bunch of numbers (to be multiplied, divided, and simplified) and the units "feet per (over, divided by) seconds". Then apply the same process to your own exercise.
