A determine the position and velocity functions for

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(a) Determine the position and velocity functions for the coin. (b) Determine the average velocity of the interval [1, 2]. (c) Find the instantaneous velocities at t = 1 and t = 2. (d) Find the time required for the coin to reach ground level. (e) Find the velocity of the coin at impact. 4. Use the position function s(t) = -4.9t 2 + v o t + s o for free-falling objects. A projectile is shot upward from the surface of Earth with an initial velocity of 120 meters per second. a. What is the velocity after 5 seconds? After 10 seconds? b. Determine the acceleration at any given time. c. What is the highest point that the projectile reaches?
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5. A particle moves along a horizontal line according to graph of s(t). (s is in cm. and t is in seconds) a) When is particle at rest? b) When does particle move left? c) When does particle move right? d) Graph the velocity. e) Graph the speed. f) Graph the acceleration.
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Find dx dy for each function. SIMPLIFY. 6. y = 5 2 x 7 - 6 3 x 7. y = 3 x - 5 3 2 x 6.________________________ 7.________________________ 8. y = 2 5 7 3 x x - + 9. y = (5x 2 – 4)(3 + x 7 ) 8. _________________________ 9. __________________________ 10. 2. y = 5 3 3 x + 2 2 x + 3 2 x + 11 11. y = (x 4 - 4 1 x )(x 2 + 2) 10. ___________________________ 11. ___________________________ 12. y = 1 4 1 2 3 3 2 + + - x x x 13. y = 3 x (5x 3 – 9x 2 + 3)
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12. ___________________________ 13. ___________________________ 14. A particle moves along a horizontal line according to s(t) = -1/3t 3 + t – 2/3, where t ≥ 0 , s is in cm and t is in seconds. a. What is the particles displacement in the first 5 seconds? b. What is the particles average velocity in the first 5 seconds? c. When is the particle moving (a) left? (b) right? (c) standing still? d. When is the particle (a) speeding up? (b) slowing down? e. Sketch the particle path along a coordinate line and describe the motion.
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