The position of a particle moving along the x axis is given by x=3.0t^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?

Do you know how to find the max or min of a function by setting its derivative equal to zero? In this case the function you need to find the max of is the velocity equation - do you know how to derive velocity from the position equation you've been given?

Do you know how to find the max or min of a function by setting its derivative equal to zero? In this case the function you need to find the max of is the velocity equation - do you know how to derive velocity from the position equation you've been given?

Yes I think so. I got dx/dt = 6t -3t^2 .
Then 6t - 3t^2 = 0
T = 0 , t= 2
Is this correct so far?

Yes I think so. I got dx/dt = 6t -3t^2 .
Then 6t - 3t^2 = 0

This would help you find the time when velocity =0, but what you want is the time when the derivative of velocity (in other wprds, its acceleration) =0, because that is when velocity is a local max or min. So you need to take the derivatove of the velocity function and set it to zero.