1.36: A particle is moving in a straight line.

A particle $\displaystyle P$ is moving in a straight line. The displacement $\displaystyle s$ of $\displaystyle P$, in metres, at time $\displaystyle t$ seconds, $\displaystyle t \geq 0$, is given by

At time $\displaystyle t = 0$, $\displaystyle P$ is at the point $\displaystyle A$ and at time $\displaystyle t = \frac{\pi}{6}$, $\displaystyle P$ is at the point $\displaystyle B$

(a) Find the exact distance $\displaystyle AB$

(b) Find the exact velocity of $\displaystyle P$ when $\displaystyle t = \frac{\pi}{3}$