Question

A particle moves according to a law of motion s = f(t), t ≥ 0, where...

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) = t3 − 8t2 + 23t

(a) Find the velocity at time t.
v(t) =    ft/s

(b) What is the velocity after 1 second?
v(1) =   ft/s

(c) When is the particle at rest?



(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)



(e) Find the total distance traveled during the first 6 seconds.

  ft

(f) Draw a diagram like this figure to illustrate the motion of the particle.


(g) Find the acceleration at time t and after 1 second.

a(t) =   ft/s2
a(1) =   ft/s2



(h) Graph the position, velocity, and acceleration functions for

0 ≤ t ≤ 6.

(A graphing calculator is recommended.)


(i) When is the particle speeding up? (Enter your answer using interval notation.)



When is it slowing down? (Enter your answer using interval notation.)

Math   Calculus   
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