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2.2 Position Velocity and Acceleration Objective: Use derivatives to find rates of change

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## 2.2 Position Velocity and Acceleration Objective: Use derivatives to find rates of change

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**2.2 Position Velocity and AccelerationObjective: Use**derivatives to find rates of change Ms. Battaglia AB Calculus**Rates of Change**• Derivatives can be used to determine the rate of change of one variable with respect to another. • Examples: population growth rates, production rates, water flow rates, velocity, and acceleration.**Rates of Change**The function s that gives the position (relative to the origin) of an object as a function of time t is called a position function. the average velocity is**Finding Average Velocity of a Falling Object**If a billiard ball is dropped from a height of 100 ft, its height s at time t is given by the position function where s is measured in ft and t is measured in sec. Find the average velocity over each of the following time intervals. a. [1,2] b. [1,1.5] c. [1,1.1]**Suppose you wanted to find the instantaneous velocity of the**object at t=1. • The velocity of the object at time t is • The speed of an object is the absolute value of its velocity (can’t be negative). • The position of a free-falling object under the influence of gravity is where is the initial height of the object, is the initial velocity of the object, and g is the acceleration due to gravity.**Using the Derivative to Find Velocity**At a time t=0, a diver jumps from a platform diving board that is 32 ft above the water. The position of the diver is given by where s is measured in ft and t is measured in sec. • When does the diver hit the water? • What is the diver’s velocity at impact?**Example**• Find the average rate of change of the function over the given interval. Compare this average rate of change with instantaneous rates of change at the endpoints of the interval. [1,2]**Example**• Find the average rate of change of the function over the given interval. Compare this average rate of change with instantaneous rates of change at the endpoints of the interval. [3,3.1]**Example**• Find the average rate of change of the function over the given interval. Compare this average rate of change with instantaneous rates of change at the endpoints of the interval.**Classwork/Homework**• Page 97-100, worksheet