5

5. [Maximum mark: 7]

A particle P moves in a straight line. The velocity $v \text{ ms}^{-1}$ of P, at time $t$ seconds is given by $v(t) = e^{-\sin t} \cos(2t)$, for $0 \le t \le 5$.

(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]