2. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors in a horizontal plane.] Three forces, \(( - 10 \mathbf { i } + a \mathbf { j } ) \mathrm { N } , ( b \mathbf { i } - 5 \mathbf { j } ) \mathrm { N }\) and \(( 2 a \mathbf { i } + 7 \mathbf { j } ) \mathrm { N }\), where \(a\) and \(b\) are constants, act on a particle \(P\) of mass 3 kg . The acceleration of \(P\) is \(( 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\)

1. Find the value of \(a\) and the value of \(b\). At time \(t = 0\) seconds the speed of \(P\) is \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and at time \(t = 4\) seconds the velocity of \(P\) is \(( 20 \mathbf { i } + 20 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
2. Find the value of \(u\).