2. A particle \(P\) is moving with constant acceleration along a straight horizontal line \(A B C\), where \(A C = 24 \mathrm {~m}\). Initially \(P\) is at \(A\) and is moving with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction \(A B\). After 1.5 s , the direction of motion of \(P\) is unchanged and \(P\) is at \(B\) with speed \(9.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that the speed of \(P\) at \(C\) is \(13 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The mass of \(P\) is 2 kg . When \(P\) reaches \(C\), an impulse of magnitude 30 Ns is applied to \(P\) in the direction \(C B\).
2. Find the velocity of \(P\) immediately after the impulse has been applied, stating clearly the direction of motion of \(P\) at this instant.
   (3)