A brick of mass 3 kg slides in a straight line on a horizontal floor. The brick is modelled as a particle and the floor as a rough plane. The initial speed of the brick is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The brick is brought to rest after moving 12 m by the constant frictional force between the brick and the floor.
Calculate the kinetic energy lost by the brick in coming to rest, stating the units of your answer.
Calculate the coefficient of friction between the brick and the floor.
A particle \(P\) of mass 0.4 kg is moving so that its position vector \(\mathbf { r }\) metres at time \(t\) seconds is given by
$$\mathbf { r } = \left( t ^ { 2 } + 4 t \right) \mathbf { i } + \left( 3 t - t ^ { 3 } \right) \mathbf { j } .$$
Calculate the speed of \(P\) when \(t = 3\).
When \(t = 3\), the particle \(P\) is given an impulse ( \(8 \mathbf { i } - 12 \mathbf { j }\) ) N s.
Find the velocity of \(P\) immediately after the impulse.