A constant force, \(\mathbf { F }\), acts on a particle, \(P\), of mass 5 kg causing its velocity to change from \(\left( { } ^ { - } 2 \mathbf { i } + \mathbf { j } \right) \mathrm { ms } ^ { - 1 }\) to \(( 4 \mathbf { i } - 7 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) in 2 seconds.
Find, in the form \(a \mathbf { i } + b \mathbf { j }\), the acceleration of \(P\).
Show that the magnitude of \(\mathbf { F }\) is 25 N and find, to the nearest degree, the acute angle between the line of action of \(\mathbf { F }\) and the vector \(\mathbf { j }\).
(5 marks)
A particle \(A\) of mass \(3 m\) is moving along a straight line with constant speed \(u \mathrm {~ms} ^ { - 1 }\). It collides with a particle \(B\) of mass \(2 m\) moving at the same speed but in the opposite direction. As a result of the collision, \(A\) is brought to rest.
Show that, after the collision, \(B\) has changed its direction of motion and that its speed has been halved.
Given that the magnitude of the impulse exerted by \(A\) on \(B\) is \(9 m \mathrm { Ns }\),