calclec8

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1 tom.h.wilson [email protected] Tom Wilson, Department of Geology and Geography Dept. Geology and Geography West Virginia University Recall how we estimate distance covered when velocity varies continuously with time: v = kt 2 kt 2 ktdt C  This is an indefinite integral. The result indicates that the starting point is unknown; it can vary. To know Tom Wilson, Department of Geology and Geography where the thing is going to be at a certain time, you have to know where it started. You have to know C.

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2 v=nt 20 40 60 80 100 velocity vk t dx v dt dx vdt dx vdt  The instantaneous velocity 0 024681 0 time 100 150 cation 2 2 kt vdt C  2 2 kt is the area under the curve vdt Tom Wilson, Department of Geology and Geography 0 50 01234 time loc x5 x6 x7 x8 is the area under a curve, but there are lots of “areas” that when differentiated yield the same v. v=kt Tom Wilson, Department of Geology and Geography The velocity of the object doesn’t depend on the starting point (that could vary)– just on the elapsed time.
3 100 150 location 0 50 01234 time x6 x7 x8 but - location as a function of time obviously does depend on the Tom Wilson, Department of Geology and Geography starting point. 2 2 kt C 100 150 2 kt C 0 50 time You just add your starting distance ( C ) to 2 2 2 kt Tom Wilson, Department of Geology and Geography That will predict the location accurately after time t

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4 There’s another class of integrals in which the limits of integration are specified, such as 2 T T
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calclec8 - tom.h.wilson [email protected] Dept...

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