Greg Kelly, Hanford High School, Richland, Washington.

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Presentation transcript:

Greg Kelly, Hanford High School, Richland, Washington

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 100ft 700 feet

What is the displacement of the bee? 200ft -200ft 200ft -100ft 100 feet towards the hive

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. 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.

velocity graph position graph Displacement: Distance Traveled: AP exams often have problems requiring students to interpret velocity and position graphs.

Example: Given: Find the position function

Example: Given: Find the displacement and the total distance traveled from t = 0 to t = 5 seconds

Example: Little kids think it is pretty neat to throw objects off of high places. If the younger Mike Efram threw a penny off of the roof of the UCSB Physics building (120 ft high) with an initial velocity of 40 ft/sec: Using the formula: a)How long would it take for the penny to hit the ground? b)What would be the velocity of the penny when it hit the ground? (in ft./sec.) c)What is the penny’s maximum height?