Particle Motion: Zero Velocity and Distance Traveled at x=0

[Alexanddros81]

Homework Statement

11.8 The motion of a particle is defined by the relation ##x=t^3 - 6t^2 - 36t - 40,
where x and t are expressed in feet and seconds, respectively. Determine
(a) when the velocity is zero, (b) the velocity, the acceleration, and the total
distance traveled when x = 0.

Homework Equations

The Attempt at a Solution

[/B]
Can you check my solution?

 

[TSny]

It all looks correct to me. I'm not sure why you found the time when $a = 0$ or the position at that time.