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6. A particle moves according to a law of motion s(t) = t³-12t² +36t, t≥0, where t is in seconds and s in meters. (a) Find the velocity at time t. (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in positive direction? (e) Find the total distance traveled during the first 8 s. (f) Draw a diagram illustrating the motion of the particle. (g) Find the acceleration at time t and after 3 s. (h) Graph the position, velocity and acceleration functions for 0≤t≤8. (i) When is the particle speeding up? When is it slowing down?

6. A particle moves according to a law of motion s(t) = t³-12t² +36t, t≥0, where t is in seconds and s in meters. (a) Find the velocity at time t. (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in positive direction? (e) Find the total distance traveled during the first 8 s. (f) Draw a diagram illustrating the motion of the particle. (g) Find the acceleration at time t and after 3 s. (h) Graph the position, velocity and acceleration functions for 0≤t≤8. (i) When is the particle speeding up? When is it slowing down?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve part d, f, h, and i with explanation. Thanks
6. A particle moves according to a law of motion s(t) = t³-12t² +36t, t≥0, where t is in seconds and s in meters. (a) Find the velocity at time t. (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in positive direction? (e) Find the total distance traveled during the first 8 s. (f) Draw a diagram illustrating the motion of the particle. (g) Find the acceleration at time t and after 3 s. (h) Graph the position, velocity and acceleration functions for 0≤t≤8. (i) When is the particle speeding up? When is it slowing down?
Transcribed Image Text:6. A particle moves according to a law of motion s(t) = t³-12t² +36t, t≥0, where t is in seconds and s in meters. (a) Find the velocity at time t. (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in positive direction? (e) Find the total distance traveled during the first 8 s. (f) Draw a diagram illustrating the motion of the particle. (g) Find the acceleration at time t and after 3 s. (h) Graph the position, velocity and acceleration functions for 0≤t≤8. (i) When is the particle speeding up? When is it slowing down?
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