For a particle the displacement–time relation is (in metres

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For a particle the displacement–time relation is

x(t) = t^{3} - 6t^{2} + 9t

(in metres,

t

in seconds). (i) Find the instants when the particle reverses its direction of motion. (ii) Determine the displacement of the particle between

t = 0

and

t = 6\,\text{s}