  We restrict purely kinetic k-essence. Assuming the equation of state is a
power law of the kinetic energy: $w=w_0X^{\alpha}$, to obtain accelerated
phases, we must have $\alpha>0$ as one of necessary conditions, constrained
from the conditions for stability and causality, and the k-essence must behave
like phantom. We also study the evolutions of the equation of state and the
speed of sound with numerical simulation.
