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

\(s=1.5\mathrm e^{2t}+2\mathrm e^{-2t}-t.\)

(a) Find expressions for the velocity, \(v\text{ m s}^{-1}\), and acceleration, \(a\text{ m s}^{-2}\), of the particle.

(b) Find the time, \(T\) seconds, when the particle is at rest.

(c) Find the acceleration of the particle at time \(T\) seconds.