Finding position/movement of a particle along a horizontal coordinate line given a specific function?

Question

One of the practice problems in my book states: A particle moves according to a law of motion $s=f(t) __ [m], t>=0$, where $t$ is seconds. A particle moves along a horizontal coordinate line in such a way that its position at time $t$ is specified by $s(t)=t^3-12t^2+36t-30$:

• a) When is the particle standing still?
• b) When does the particle move left?
• c) When does the particle move right?
• d) Find the total distance traveled during the first 10 seconds.

(If I'm understanding this correctly) I would plug in $0$ for $t$ to answer (a) and then do the same with $10$ for $t$ to answer (d), but how do I answer (b) & (c)? Or am I missing something with (a) & (d) as well?

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EDIT:

Taking Ross's suggestion, for (a) I have the following:

$s(t)=t^3-12t^2+36t-30$
$s'(t)=3t^2-24t+36$
$s'(0)=3(0)^2-24(0)+36$
$s'(0)=36$?

Still not sure what to do in order to answer (b), (c), (d)?

Answer 1

The particle is standing still when the velocity is zero. The velocity is the time derivative of the position, so for a, you want $s'(t)=0$. For b and c you want the derivative to have the proper sign. The total distance traveled comes from integrating the absolute value of the velocity to account for back and forth motion

Answer 2

Draw the graph of s'(t) ; positive means it moves right; zero means stand-still. negative means it moves to left.

Find s(10) for distance traveled.