- \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors.]
A particle \(P\) of mass 2 kg moves under the action of two forces, \(( 2 \mathbf { i } + 3 \mathbf { j } ) \mathrm { N }\) and \(( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { N }\).
- Find the magnitude of the acceleration of \(P\).
At time \(t = 0 , P\) has velocity ( \(- u \mathbf { i } + u \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\), where \(u\) is a positive constant.
At time \(t = T\) seconds, \(P\) has velocity \(( 10 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
- Find
- the value of \(T\),
- the value of \(u\).