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Calc07_1 - Photo by Vickie Kelly 2006 Greg Kelly Hanford...

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Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2006
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ft min minutes A honey bee makes several trips from the hive to a flower garden. The velocity graph is shown below. What is the total distance traveled by the bee? 200ft 200ft 200ft 100ft 200 200 200 100 700 + + + = 700 feet
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ft min minutes What is the displacement of the bee? 200ft -200ft 200ft -100ft 200 200 200 100 100 - + - = 100 feet towards the hive
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To find the displacement (position shift) from the velocity function, we just integrate the function. The negative areas below the x-axis subtract from the total displacement. ( 29 Displacement b a V t dt = ( 29 Distance Traveled b a V t dt = To find distance traveled we have to use absolute value. Find the roots of the velocity equation and integrate in pieces, just like when we found the area between a curve and the x-axis. (Take the absolute value of each integral.) Or you can use your calculator to integrate the absolute value of the velocity function.
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