A particle \(P\) of mass 2 kg is moving under the action of a constant force \(\mathbf { F }\) newtons. When \(t = 0 , P\) has velocity ( \(3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and at time \(t = 4 \mathrm {~s} , P\) has velocity \(( 15 \mathbf { i } - 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find
the acceleration of \(P\) in terms of \(\mathbf { i }\) and \(\mathbf { j }\),
the magnitude of \(\mathbf { F }\),
the velocity of \(P\) at time \(t = 6 \mathrm {~s}\).
A particle \(P\) of mass 0.3 kg is moving with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a straight line on a smooth horizontal table. The particle \(P\) collides directly with a particle \(Q\) of mass 0.6 kg , which is at rest on the table. Immediately after the particles collide, \(P\) has speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(Q\) has speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The direction of motion of \(P\) is reversed by the collision. Find
the value of \(u\),
the magnitude of the impulse exerted by \(P\) on \(Q\).
Immediately after the collision, a constant force of magnitude \(R\) newtons is applied to \(Q\) in the direction directly opposite to the direction of motion of \(Q\). As a result \(Q\) is brought to rest in 1.5 s .