A stone \(S\) is sliding on ice. The stone is moving along a straight horizontal line \(A B C\), where \(A B = 24 \mathrm {~m}\) and \(A C = 30 \mathrm {~m}\). The stone is subject to a constant resistance to motion of magnitude 0.3 N . At \(A\) the speed of \(S\) is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and at \(B\) the speed of \(S\) is \(16 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Calculate
the deceleration of \(S\),
the speed of \(S\) at \(C\).
Show that the mass of \(S\) is 0.1 kg .
At \(C\), the stone \(S\) hits a vertical wall, rebounds from the wall and then slides back along the line \(C A\). The magnitude of the impulse of the wall on \(S\) is 2.4 Ns and the stone continues to move against a constant resistance of 0.3 N .
Calculate the time between the instant that \(S\) rebounds from the wall and the instant that \(S\) comes to rest.