How to find the maximum velocity and maximum acceleration?

  1. 1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations

    3. 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 dont know what to do to solve for the max velocity and acceleration:confused:
  2. jcsd
  3. You have the velocity as a function of time, just like you had the position as a function of time.
  4. more hints?
  5. Why not repeat the same process for your function of velocity?
  6. Oh, so i set a=0 to find max velocity, but then what do I do to find the max acceleration?
  7. 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.
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