Mathematics

Problem

The displacement of a particle moving along the

x

-axis is given by

x(t)=3 t^{3}-6 t^{2}+2 t

(SI units). a. (i) Find the values of

t

(in the interval

0 \le t \le 3\,\text{s}

) at which the particle is momentarily at rest. b. (ii) State whether the instantaneous velocity just after

t=2\,\text{s}

is positive or negative.