A particle travels in a straight line. Its displacement, \(s\) metres, from the origin, at time \(t\) seconds, where \(t\gt2\), is given by

\(s=\ln(4t^2-5)-t.\)

(a) Find an expression for the velocity, \(v\), and show that the acceleration, \(a\), is given by

\(a=-\frac{8(4t^2+5)}{(4t^2-5)^2}.\)

(b) Find the exact value of \(t\) when the particle is at rest.

(c) Find the exact value of the acceleration when the particle is at rest.