Calculating Average Speed Based on Distance and Time

In physics, average speed is the total distance you travel divided by the total time it takes. Speed is represented by the variable v, and average speed is sometimes written as

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A bar over a variable means average in physics terms.

Say, for example, that you want to pound the pavement from New York City to Los Angeles to visit your uncle’s family, a distance of about 2,781 miles. If the trip takes you 4.000 days, what was your average speed? You divide the total distance by the change in time, so your average speed for the trip would be

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This solution divides miles by days, so you come up with 695.3 miles per day. Not exactly a standard unit of measurement — what’s that in miles per hour? To find it, you want to cancel days out of the equation and put in hours. Because a day is 24 hours, you can multiply this way (note that days cancels out, leaving miles over hours, or miles per hour):

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That’s a better answer.

You can relate total distance traveled, s, with average speed,

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and time, t, like this:

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