A tennis ball of mass 0.1 kg is hit by a racquet. Immediately before being hit, the ball has velocity \(30 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The racquet exerts an impulse of \(( - 2 \mathbf { i } - 4 \mathbf { j } ) \mathrm { Ns }\) on the ball. By modelling the ball as a particle, find the velocity of the ball immediately after being hit.
A particle \(P\) is moving in a plane. At time \(t\) seconds, \(P\) is moving with velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(\mathbf { v } = 2 t \mathbf { i } - 3 t ^ { 2 } \mathbf { j }\).
Find
the speed of \(P\) when \(t = 4\)
the acceleration of \(P\) when \(t = 4\)
Given that \(P\) is at the point with position vector \(( - 4 \mathbf { i } + \mathbf { j } ) \mathrm { m }\) when \(t = 1\),