Mathematics

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

. a. Find the maximum speed of P. [2] b. Find the total distance travelled by P. [2] c. Find the acceleration when

P

changes direction for the second time. [3]