- #1

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I am at the noob end of calculus so trying to grasp how to interpret things like dv/dt or what what dv would mean if it were standing alone.

TIA

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- #1

- 36

- 0

I am at the noob end of calculus so trying to grasp how to interpret things like dv/dt or what what dv would mean if it were standing alone.

TIA

- #2

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2. Now, dv/dt is what we call the instantaneous rate of change in "v", that is the limit of "delta v"/"delta t" as we let the time interval "delta t" shrink to zero.

- #3

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[tex]\dfrac{dx}{dt}= \lim_{\Delta t \to 0}\dfrac{\Delta x}{\Delta t}[/tex]

Calculus texts typically spend a good deal of time on the "limit" concept.

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This tells you nothing about the velocity at any given moment. The car likely started at 0, gained speed up to a certain point, stopped for a light, got lost and had to go back a block, etc. So if you want to know how fast the car was traveling, and in what direction, at any given moment, ## \Delta x/ \Delta t ## tells you almost nothing.

But if you look at the average velocity of a small time period, that is closer to the velocity at any given time ##t_0## in the period. Make the time period smaller yet, and you are closer yet to the velocity at ##t_0##.

The genius of calculus was to see that you can let that time interval go to 0 and ## \Delta x/ \Delta t## may "converge" to a simple number -- say 30 mph. That is dx/dt -- the instantaneous velocity.

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