Average Velocity and Instantaneous Velocity

# Average Velocity and Instantaneous Velocity - with position...

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Average Velocity and Instantaneous Velocity Now that we have a better grasp of what velocity is, we can more precisely define its relationship to position. Average Velocity We begin by writing down the formula for average velocity. The average velocity of an object with position function x ( t ) over the time interval ( t 0 , t 1 ) is given by: v avg = In other words, the average velocity is the total displacement divided by the total time. Notice that if a car leaves its garage in the morning, drives all around town throughout the day, and ends up right back in the same garage at night, its displacement is 0, meaning its average velocity for the whole day is also 0. Instantaneous Velocity As the time intervals get smaller and smaller in the equation for average velocity, we approach the instantaneous velocity of an object. The formula we arrive at for the velocity of an object
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Unformatted text preview: with position function x ( t ) at a particular instant of time t is thus: v ( t ) = This is, in fact, the formula for the velocity function in terms of the position function! (In the language of calculus, this is also known as the formula for the derivative of x with respect to t . ) Unfortunately, it is not feasible, in general, to compute this limit for every single value of t. However, the position functions we will be dealing with in this SparkNote (and those you will likely have to deal with in class) have exceptionally simple forms, and hence it is possible for us to write down their corresponding velocity functions in terms of a single rule valid for all time. In order to do this, we will borrow some results from elementary calculus. These results will also prove useful in our discussion of acceleration....
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