A particle P moves in a straight line

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

Problem

A particle P moves in a straight line. The velocity

v \text{ m s}^{-1}

of P, at time

t

seconds is given by

v(t) = e^{-\sin t} \cos(2t)

, for

0 \leq t \leq 5

. (1) Find the maximum speed of P. [2] (2) Find the total distance travelled by P. [2] (3) Find the acceleration when

P

changes direction for the second time. [3]