Lecture 2: 09/8/11
note: text in red refers to the textbook, 9
th
edition extended.
1. Average Velocity and Speed
–
section
24
2. Instantaneous velocity  section
25
3. Derivatives The average velocity of a particle between time t and t+dt is
( )
(
) ( )
(
)
As the time interval dt becomes smaller, you get a more accurate answer for the velocity at time t. The
instantaneous velocity (or simply, velocity at time t) is obtained in the mathematical limit where the
time dt goes to zero:
( )
(
) ( )
(
)
( )
You can use this definition of the derivative to calculate the derivative of functions. In the class we will
mostly use the following results
(and other trig functions). To a lesser extent:
These formulae can all be derived from the limit formula for the derivative. Please make sure you are
comfortable with this. We will also use the following rules for derivatives
(
)
( )
where
refers to the derivative of
4. Acceleration 
section
26
5. Special Case of Acceleration
–
section
27
.
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 Spring '11
 DODD
 Calculus, Derivative, Velocity

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