Question

f(t)=t^{3}-9 t^{2}+24 t A graphing calculator is recommended. A particle moves according to a law of motion s = f(t), t > 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) (a) Find the velocity (in ft/s) at time t. (b) What is the velocity (in ft/s) after 1 second? (c) When is the particle at rest? (Enter your answers as a comma-separated list.) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. (f) Find the acceleration (in ft/s^2) at time t. Find the acceleration (in ft/s^2) after 1 second. (g) Graph the position, velocity, and acceleration functions for 0 <= t <= 6. (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down?

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9

Fig: 10

Fig: 11

Fig: 12

Fig: 13

Fig: 14

Fig: 15

Fig: 16