Calculus
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.)
f(t)=t^{3}-9 t^{2}+24 t
(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?
Verified
Getting answers to your urgent problems is simple. Submit your query in the given box and get answers Instantly.
Success