1. Two particles \(A\) and \(B\), of masses 2 kg and 5 kg respectively, are moving in the same direction along a smooth horizontal surface when they collide directly. Before the collision, \(B\) is moving with speed \(1.2 \mathrm {~ms} ^ { - 1 }\) and, immediately after the collision, its speed is \(3.8 \mathrm {~ms} ^ { - 1 }\). The coefficient of restitution between the particles \(A\) and \(B\) is 0.3 .

1. 1. Find the impulse exerted by \(A\) on \(B\).
   2. Given that the particles \(A\) and \(B\) were in contact for 0.08 seconds, find the average force between \(A\) and \(B\).
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2. Calculate the speed of \(A\) before and after the collision.
3. After the collision between \(A\) and \(B\), particle \(B\) continues to move with speed \(3.8 \mathrm {~ms} ^ { - 1 }\) until it collides directly with a stationary particle \(C\) of mass 4 kg . When \(B\) and \(C\) collide, they coalesce to form a single particle.
   1. Write down the coefficient of restitution between \(B\) and \(C\).
   2. Determine the speed of the combined particle after the collision.
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