Find the velocity vector of \(P\) at time \(t\) seconds.
Show that the direction of the acceleration of \(P\) is constant.
Find the value of \(t\) when the acceleration of \(P\) has magnitude \(12 \mathrm {~ms} ^ { - 2 }\).
\item A uniform plank of wood \(X Y\), of mass 1.4 kg , rests with its upper end \(X\) against a rough vertical wall and its lower end \(Y\) on rough horizontal ground. The coefficient of friction between the plank and both the wall and the ground is \(\mu\). The plank is in limiting equilibrium at both ends and the vertical component of the force exerted on the plank by the ground has magnitude 12 N .
Find the value of \(\mu\), to 2 decimal places.
\item A motor-cycle and its rider have a total mass of 460 kg . The maximum rate at which the cycle's engine can work is 25920 W and the maximum speed of the cycle on a horizontal road is \(36 \mathrm {~ms} ^ { - 1 }\). A variable resisting force acts on the cycle and has magnitude \(k v ^ { 2 }\), where \(v\) is the speed of the cycle in \(\mathrm { ms } ^ { - 1 }\).
Show that \(k = \frac { 5 } { 9 }\).
Find the acceleration of the cycle when it is moving at \(25 \mathrm {~ms} ^ { - 1 }\) on the horizontal road, with its engine working at full power.
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\section*{MECHANICS 2 (A)TEST PAPER 8 Page 2}