3．At time \(t\) seconds（ \(t \geqslant 0\) ）a particle \(P\) has velocity \(\mathbf { v } \mathrm { ms } ^ { - 1 }\) ，where When \(t = 0\) the particle \(P\) is at the origin \(O\) ．At time \(T\) seconds，\(P\) is at the point \(A\) and \(\mathbf { v } = \lambda ( \mathbf { i } + \mathbf { j } )\) ，where \(\lambda\) is a constant． Find
（a）the value of \(T\) ，
（b）the acceleration of \(P\) as it passes through the point \(A\) ，
（c）the distance \(O A\) ． $$\mathbf { v } = \left( 6 t ^ { 2 } + 6 t \right) \mathbf { i } + \left( 3 t ^ { 2 } + 24 \right) \mathbf { j }$$ 的 When \(t = 0\) the particle \(P\) is at the origin \(O\) ．At time \(T\) seconds，\(P\) is at the point \(A\) and
\(\mathbf { v } = \lambda ( \mathbf { i } + \mathbf { j } )\) ，where \(\lambda\) is a constant． Find
（a）the value of \(T\) ，
\(\_\_\_\_\) ＂