SEMANTICS OF THE DIFFERENTIAL CALCULUS 591 |
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4.
VELOCITYUntil now we have treated our independent variables as
any quantity: but there are many problems where the independent variable represents 'time'. For instance, if we travel by railroad the distance increases as 'time' increases, plants and animals grow with 'time', . By the average velocity with which a given point moves for a given length of 'time' we mean the distance s traversed divided by the 'time' elapsed. If, for instance, a train makes 5 miles in 10 minutes we say that its average velocity is 30 miles per hour, or, in symbols: |
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