7. Two particles \(A\) and \(B\), of mass \(3 M \mathrm {~kg}\) and \(2 M \mathrm {~kg}\) respectively, are moving towards each other on a rough horizontal track. Just before they collide, \(A\) has speed \(3 \mathrm {~ms} ^ { - 1 }\) and \(B\) has speed \(5 \mathrm {~ms} ^ { - 1 }\). Immediately after the impact, the direction of motion of both particles has been reversed and they are both travelling at the same speed, \(v\).
- Show that \(v = 1 \mathrm {~ms} ^ { - 1 }\).
The magnitude of the impulse exerted on \(A\) during the collision is 24 Ns.
- Find the value of \(M\).
Given that the coefficient of friction between \(A\) and the track is 0.1 ,
- find the time taken from the moment of impact until \(A\) comes to rest.
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