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.)
[tex]f(t) = t^3 - 9t^2 + 24t[/tex]
(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/s2) at time t.
(g)
When is the particle speeding up? (Enter your answer using interval notation.)
(h)
When is it slowing down? (Enter your answer using interval notation.)