A particle \(P\) moves in a straight line. The velocity \(v\text{ m s}^{-1}\) of \(P\) at time \(t\text{ s}\), where \(t\geq0\), is given by

\[ v=k_1(4t+1)^{\frac12}-\frac14(2t+1)^2+k_2, \]

where \(k_1\) and \(k_2\) are constants. When \(t=1.25\) the deceleration of \(P\) is \(0.5\text{ m s}^{-2}\).

(a) Find the value of \(k_1\).

(b) Given that \(P\) is only at instantaneous rest when \(t=3.5\), find the distance travelled by \(P\) in the interval \(0\leq t\leq1\).