What is the position of a particle at maximum speed?

[jrrodri7]

Homework Statement

The position of a particle moving along the x-axis is given by

x = 6.0t^{2} - 1.0t^{3} , where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?

Homework Equations

motion equations and derivative/integration ideas from motion.

The Attempt at a Solution

 

[Dick]

You forgot to attempt a solution. Please try?

 

[jeffreydk]

How do you think you would get velocity from that expression?

 

[Dick]

You are given position as a function of time. How is velocity related to position? I think you mentioned derivatives/integrals as things to use.

 

[jrrodri7]

ya i figured the derivative of position is velocity right, but I tried doing that and then using that as galileo's equation of motion, substituting the 12 and 3 for velocity and acceleration...but i kept getting numbers that didn't make sense.

 

[Dick]

Yes, the derivative of the position is the velocity. Now how would you maximize it? Your description of what you did isn't very clear. Can you write it out completely, showing those numbers that 'don't make sense'?

 

[jrrodri7]

the derivative is 12t - 3t^(2). That is velocity, now to maximize the equation take the derivative of it? and use that to plug into the other one?

 

[Dick]

Yes, to maximize something you take it's derivative and set it equal to zero. In this case you are setting the acceleration equal to zero. At maximum velocity, the acceleration is zero.