- At time \(t\) seconds, a particle \(P\) has position vector \(r\) metres relative to a fixed origin \(O\), where
$$\mathbf { r } = \left( t ^ { 2 } + 2 t \right) \mathbf { i } + \left( t - 2 t ^ { 2 } \right) \mathbf { j } .$$
Show that the acceleration of \(P\) is constant and find its magnitude.
\section*{2.}
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\caption{Figure 1}
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Figure 1 shows a decoration which is made by cutting 2 circular discs from a sheet of uniform card. The discs are joined so that they touch at a point \(D\) on the circumference of both discs. The discs are coplanar and have centres \(A\) and \(B\) with radii 10 cm and 20 cm respectively.
- Find the distance of the centre of mass of the decoration from B.
The point \(C\) lies on the circumference of the smaller disc and \(\angle C A B\) is a right angle. The decoration is freely suspended from C and hangs in equilibrium.
- Find, in degrees to one decimal place, the angle between AB and the vertical.