How to find the maximum velocity and maximum acceleration?

[dumpman]

Homework Statement

The position of a particle moving along an x-axis is given by x=12t^2-2t^3, what is the maximum positive coordinate, velocity and acceleration reached by the particle?

Homework Equations

The Attempt at a Solution

I took derivative of the quadratic and got V=24t-6t^2 and set it =0, then i solve for t and substituted in x=12t^2-2t^3 to get the max. positive coordinate.
But I don't know what to do to solve for the max velocity and acceleration

 

[Mindscrape]

You have the velocity as a function of time, just like you had the position as a function of time.

 

[dumpman]

more hints?

 

[Mindscrape]

Why not repeat the same process for your function of velocity?

 

[dumpman]

Oh, so i set a=0 to find max velocity, but then what do I do to find the max acceleration?

 

[Mindscrape]

Find the derivative of acceleration as a function of time and set it to zero. The physical term for the fourth derivative time is called jerk.