A particle travelling in a straight line passes through a fixed point \(O\). The displacement, \(x\) metres, of the particle, \(t\) seconds after it passes through \(O\), is given by \(x=5t+\sin t\).

(i) Show that the particle is never at rest.

(ii) Find the distance travelled by the particle between \(t=\dfrac{\pi}{3}\) and \(t=\dfrac{\pi}{2}\).

(iii) Find the acceleration of the particle when \(t=4\).

(iv) Find the value of \(t\) when the velocity of the particle is first at its minimum.