A particle \(P\) travels in a straight line. The velocity of \(P\) at time \(t\text{ s}\) is \(v\text{ m s}^{-1}\), where

\[ v=t-7t^{\frac12}+12. \]

(a) Find the acceleration of \(P\) at \(t=4\).

(b) Find the values of \(t\) at which \(P\) is instantaneously at rest.

(c) Find the total distance travelled by \(P\) in the interval \(0\leq t\leq25\).