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lecture3_9_13_11 - Lecture 3 note text in red refers to the...

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Lecture 3: 09/13/11 note: text in red refers to the textbook, 9 th edition extended. 1. Obtaining position from velocity section 2-10 Starting with the definition of velocity ( ) ( ) ( ) ( ) rearrange to get: ( ) ( ) ( ) ie, the increment in the position between time t and t+dt is given by the product of the velocity at t and the time interval dt. This is true for small intervals of time dt. We can therefore get the position at a time t 2 relative to an initial position t 1 by breaking the time interval into little bits of time and adding ( ) for each bit of time. ( ) ( ) ∑ ( ) ( ) (definition of the integral). Graphically, this is the area under the v-t curve between t 1 and t 2 2. Integral as an antiderivative - section 2-8 Given the velocity as a function of time ( ) , the position as a function of time ( ) is ( ) ∫ ( ) where c is an arbitrary constant. The integral of a function can therefore be defined as an antiderivative the integral of a function results in a new function, such that when I take the derivative of this new
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