# Chapter 2.1 - Chapter 2.1 How Do We Measure Speed Average...

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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 !!!!
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
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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