The position of a particle as it moves along the x axis is given for t> 0 by x=(t^3 - 3t^2 +6t)m , where t in sec. where id the particle wen it achieves its minimum speed (after t=0)?

We are given with the equation of the distance of a particle expressed in  x=(t^3 - 3t^2 -6t). To get the distance where minimum speed is achieved, we get the first derivative of the equation and equate to zero. hence, dx /dt = 3t^2 - 6t - 6 = 0. t is equal to 2.73 sec. The distance then after substituting to the original equation equal to 14.37 meters.