3．A particle \(P\) moves in a horizontal plane．At time \(t\) seconds，the position vector of \(P\) is \(\mathbf { r }\) metres relative to a fixed origin \(O\) ，and \(\mathbf { r }\) is given by $$\mathbf { r } = \left( 18 t - 4 t ^ { 3 } \right) \mathbf { i } + c t ^ { 2 } \mathbf { j } ,$$ where \(c\) is a positive constant．When \(t = 1.5\) ，the speed of \(P\) is \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) ．Find
（a）the value of \(c\) ， （b）the acceleration of \(P\) when \(t = 1.5\) ． \(\mathbf { r }\) metres relative to a fixed origin \(O\) ，and \(\mathbf { r }\) is given by $$\begin{aligned} \mathbf { r } = \left( 18 t - 4 t ^ { 3 } \right) \mathbf { i } + c t ^ { 2 } \mathbf { j } ,
\text { where } c \text { is a positive constant．When } t = 1.5 \text { ，the speed of } P \text { is } 15 \mathrm {~m} \mathrm {~s} ^ { - 1 } \text { ．Find } \end{aligned}$$ （a）the value of \(c\) ， 3．A particle \(P\) moves in a horizontal plane．At time \(t\) seconds，the position vector of \(P\) is D墐
（b）the acceleration of \(P\) when \(t = 1.5\) ．