1-The position of a particle moving along the x axis is given by x=t^2-〖2t〗^3-6, 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?

Answer 1

x = t^2 - (2t)^3 - 6
v = 2t - 16t^2
v is maximum when a=dv/dt=0
a = 2 - 32t
now find t when a=0. Since da/dt < 0, v will be a maximum.

Answer 2

How you find - 16t^2