Accumulator

Accumulator - A car moving with initial velocity at 5 mph...

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Calculus 12 AP The Integral as Net Change and as an Accumulator Big Ideas on Velocity and Distance What do the following integrals give you? v t ( ) dt v t ( ) dt 0 5 Example 1 Given the graph of the velocity of a particle moving on the x -axis. The particle starts at x = 2 when t = 0, v 3 0 2 3 6 7 10 t –3 a) Find the net distance traveled by the particle during the trip. b) Find where the particle is at the end of the trip. b) Find the total distance traveled by the particle.

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Example 2 The velocity of a particle is given by v t ( )= t 2 - 8 t + 1 ( ) 2 cm/sec If the particle is moving along a horizontal x-axis for 0 t 5 , a) Draw the graph of the velocity function and describe the motion of the particle. [0, 5] by [–10, 30] b) Suppose the initial position of the particle is s 0 ( )= 9. What is the particle’s position at i) t = 1 sec ii) t = 5 sec c) i) Find the net distance traveled by the particle in the first 5 seconds ii) Find the total distance traveled by the particle in the first 5 seconds
Example 3

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Unformatted text preview: A car moving with initial velocity at 5 mph accelerates at the rate of a t ( ) = 2.4 t mph per second for 8 seconds. a) How fast is the car going when the 8 seconds are up? b) How far did the car travel during those 8 seconds? Example 4 From 1970 to 1980, the rate of potato consumption in a particular country was C t ( ) = 2.2 + 1.1 t millions of bushels per year, with t being years since the beginning of 1970. How many bushels were consumed from the beginning of 1972 to the end of 1973 Example 5 A pump connected to a generator operates at a varying rate, depending on how much power is being drawn from the generator to operate other machinery. The rate (gallons per minute) at which the pump operates is recorded at 5-minute intervals for one hour as shown in the table below. How many gallons were pumped during that hour? Pumping Rate Table Time (min) Rate(gal/min) 0 58 5 60 10 65 15 64 20 58 25 57 30 55 35 55 40 59 45 60 50 60 55 63 60 63...
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This note was uploaded on 02/04/2011 for the course MATH 116 taught by Professor John during the Spring '10 term at St. Michael.

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Accumulator - A car moving with initial velocity at 5 mph...

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