Parts g, h, & i A particle moves according to a law of motion s = f(t) = t³ - 15t² + 72t, t≥ 0, where t is measured in seconds and s in feet.(a) Find the velocity at time t.v(t) = 31²-30t+72ft/s(b) What is the velocity after 5 s?v(5) = -3ft/s(c) When is the particle at rest?t = 4t = 6s (smaller value)s (larger value)(d) When is the particle moving in the positive direction? (Enter your answers in ascending order. If you need to use -∞o or co, enter -INFINITY or INFINITY.)x,x )U([(1XX )(e) Find the total distance traveled during the first 9 s.X feet(f) Draw a diagram to illustrate the motion of the particle. (Do this on paper. Your instructor may ask you to turn in this graph.)(g) Find the acceleration at time t and after 5 s.a(t) =XX ft/s²a(5) =(h) Graph the position, velocity, and acceleration functions for 0 S t ≤ 9. (Do this on paper. Your instructor may ask you to turn in this graph.)(i) When is the particle speeding up? (Enter your answers in ascending order. If you need to use -∞o or ∞o, enter -INFINITY or INFINITY.)(x*)U(When is it slowing down?Xx )x,x )U( [x,x )

Answered: Image /qna-images/answer/e2470176-0437-4fb5-b014-b09d49176323.jpg

(f) Draw a diagram to illustrate the motion of the particle. (Do this on paper. Your instructor may ask you to turn in this graph.) (g) Find the acceleration at time t and after 5 s. a(t) = X X ft/s² a(5) = (h) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 9. (Do this on paper. Your instructor may ask you to turn in this graph.) (i) When is the particle speeding up? (Enter your answers in ascending order. If you need to use -∞o or ∞o, enter -INFINITY or INFINITY.) ( X When is it slowing down? *)U( x, × ) CL X. x )U( [ X, × )

(f) Draw a diagram to illustrate the motion of the particle. (Do this on paper. Your instructor may ask you to turn in this graph.) (g) Find the acceleration at time t and after 5 s. a(t) = X X ft/s² a(5) = (h) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 9. (Do this on paper. Your instructor may ask you to turn in this graph.) (i) When is the particle speeding up? (Enter your answers in ascending order. If you need to use -∞o or ∞o, enter -INFINITY or INFINITY.) ( X When is it slowing down? *)U( x, × ) CL X. x )U( [ X, × )

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 69P: A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0...

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