Chapter 2.1 - instantaneous velocity as the slope of the...

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Chapter 2.1 How Do We Measure Speed?
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Average Velocity Let be a position function of an object at time . Then the average velocity of the object on the time interval is This is just the slope of the line passing through the points !!!!
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Speed Vs. Velocity Average Velocity on : Sign of Velocity tells you if you are speeding up or speeding down Average Speed on :
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Instantaneous Velocity Same set up as before. The instantaneous velocity of the object at time is Define . Then the instantaneous velocity of the object at time can be written as
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Speed Vs. Velocity Instantaneous Velocity at : Sign of Velocity tells you if you are speeding up or speeding down Instantaneous Speed at :
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Interpretations Graphically: We can think of average velocity as the slope of the line joining the points and . This types of lines are called secant lines . We can think of
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Unformatted text preview: instantaneous velocity as the slope of the unique line that passes through the point and no other “nearby” points. Chapter 2.2 The Derivatve a± a Poin± Average Rate of Change • Let be a funcTon. ±he average rate of change on is • DeFne . ±hen the average rate of change on can be wri²en as Instantaneous Rate of Change • The instantaneous rate of change at is called the derivatve aT . • If this limit exists, we say that is diferentable aT . Interpretations • Graphically: • We can think of average rate of change as the slope of the line joining the points and . • This types of lines are called secant lines . • We can think of derivaTve as the slope unique line that passes through the point and no other “nearby” points. • Limit may not always exists....
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