Parts d, e, & f 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 )

Name: Parts d, e, & f A particle moves according to a law of motion s = f(t)
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: Parts d, e, & f 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