The displacement of a particle moving along the -axis is given by (SI units).

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

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). (i) Find the values of

t

(in the interval

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

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

t=2\,\text{s}

is positive or negative.