Precalc0110to0111-page2 - s ( ) = , meaning that y =...

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(Section 1.10: Difference Quotients) 1.10.2 PART C: AVERAGE VELOCITY The following development of average velocity will help explain the association between slope and average rate of change. Example 1 (Average Velocity) A car is driven due north 100 miles during a two-hour trip. What is the average velocity of the car? • Let t = the time (in hours) elapsed since the beginning of the trip. • Let y = st () , where s is the position function for the car (in miles). s gives the signed distance of the car from the starting position. •• The position ( s ) values would be negative if the car were south of the starting position. • Let
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Unformatted text preview: s ( ) = , meaning that y = corresponds to the starting position. Therefore, s 2 ( ) = 100 (miles). The average velocity on the time-interval a , b is the average rate of change of position with respect to time . That is, change in position change in time = s t where (uppercase delta) denotes change in = s b ( ) s a ( ) b a , a difference quotient Here, the average velocity on 0, 2 is: s 2 ( ) s ( ) 2 = 100 2 = 50 miles hour or mi hr or mph TIP 1 : The unit of velocity is the unit of slope given by: unit of s unit of t ....
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