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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?

(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?

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