ࡱ> %` bjbjNN <,,D,=/ Hhhhh.......$/h[2R. .hh.V#V#V#.hh.V#.V#V#r<-T<.h `0M8 -. /0=/-2 "2<.2<.>,V#$3..@#=/ AP Calculus name________________________p____ Position/Velocity/Acceleration Review (from Demana Waits p. 371) Calculators are allowed In Exercises 1-5, the function v(t) is the velocity in m/sec of a particle moving long the x-axis. Determine when the particle is moving to the right, to the left, and stopped. Find the particles displacement for the given time interval. Find the total distance traveled by the particle. 1.  EMBED Equation.DSMT4  2.  EMBED Equation.DSMT4  3.  EMBED Equation.DSMT4  4. An automobile accelerates from rest at  EMBED Equation.DSMT4  mph/sec for 9 seconds. a) What is its velocity after 9 seconds? b) How far does it travel in those 9 seconds? 5. A particle travels with velocity v(t) = (t 2) sin t m/sec for 0 < t < 4 sec. a) What is the particles displacement? b) What is the total distance traveled? 6. The rate of consumption of oil in the U.S. during the 1980s (in billions of barrels/year) is modeled by the function EMBED Equation.DSMT4 , where t is the number of years after January 1, 1980. Find the total consumption of oil in the U.S. from January 1, 1980 to January 1, 1990. The rate at which your home consumes electricity is measured in kilowatts. If your home consumes electricity at the rate of 1 kilowatt for 1 hour, you will be charged for 1 kilowatt-hour of electricity. Suppose that the average consumption rate for a certain home is modeled by the function  EMBED Equation.DSMT4 , where C(t) is measured in kilowatts and t is the number of hours past midnight. Find the average hourly consumption for this home, measured in kilowatt-hours. For exercises 8-12, a particle moves along the x-axis (units in cm). Its initial position at t = 0 sec is x(0) = 15. The figure shows the graph of the particles velocity v(t). The numbers are the areas of the enclosed region. 8. What is the particles displacement between t = 0 and t = c? 9. What is the total distance traveled by the particle in the same time period? 10. Give the positions of the particle at times a, b, and c. 11. Where does the particle achieve its greatest positive acceleration on the interval [0, b]? 12. Where does the particle achieve its greatest positive acceleration on the interval [0, c]? In exercises 13-16, the graph of the velocity of a particle moving on the x-axis is given. The particle starts at x = 2 when t = 0. Find where the particle is at the end of the trip. Find the total distance traveled by the particle. 13. 14.  15. 16. Key 1. a) right:  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  left:  EMBED Equation.DSMT4  b) 0 m c) 20 m 2. a) right: (0, 1) left: (1, 2) b) 4 m c) 6 m 3. a) right:  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  left:  EMBED Equation.DSMT4  b) 0 m c) 4.701 m 4.  EMBED Equation.DSMT4  a) v(9) = 63 mph b)  EMBED Equation.DSMT4  5. a)  EMBED Equation.DSMT4  m b)  EMBED Equation.DSMT4  m 6. Total Consumption =  EMBED Equation.DSMT4  billion barrels 7. 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