How to find the maximum velocity and maximum acceleration?

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Homework Help Overview

The problem involves a particle moving along an x-axis, with its position described by the equation x=12t^2-2t^3. The original poster seeks to determine the maximum positive coordinate, velocity, and acceleration of the particle.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the maximum positive coordinate by taking the derivative of the position function to derive the velocity function. They express uncertainty about how to proceed with finding maximum velocity and acceleration.
  • Some participants suggest using the same derivative approach for the velocity function to find maximum velocity.
  • Others inquire about the method for determining maximum acceleration after finding velocity.

Discussion Status

The discussion is ongoing, with participants providing hints and suggestions for further steps. There is an exploration of the relationship between position, velocity, and acceleration, but no consensus has been reached on the final approach to finding maximum values.

Contextual Notes

The original poster has not provided specific constraints or additional information regarding the problem setup, and there is a focus on the derivatives of the functions involved.

dumpman
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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:confused:
 
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You have the velocity as a function of time, just like you had the position as a function of time.
 
more hints?
 
Why not repeat the same process for your function of velocity?
 
Oh, so i set a=0 to find max velocity, but then what do I do to find the max acceleration?
 
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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