The displacement

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

Problem

The displacement, in centimetres, of a particle from an origin, O, at time

t

seconds, is given by

s(t) = t^2 \cos t + 2t \sin t

0 \le t \le 5

. (1) Find the maximum distance of the particle from O. (2) Find the acceleration of the particle at the instant it first changes direction.