Calculate the distance \(A P\) when \(P\) is instantaneously at rest for the first time, giving your answer correct to 2 decimal places.
Estimate the distance \(A P\) when \(P\) is instantaneously at rest for the second time and clearly state one assumption that you have made in making your estimate.
\item The position vector \(\mathbf { x }\) metres at time \(t\) seconds of an object of mass 3 kg may be modelled by
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$$\mathbf { x } = 3 \sin t \mathbf { i } - 4 \cos 2 t \mathbf { j } + 5 \sin t \mathbf { k }$$
Find an expression for the velocity vector \(\mathbf { v } \mathrm { ms } ^ { - 1 }\) at time \(t\) seconds and determine the least value of \(t\) when the object is instantaneously at rest.
Write down the momentum vector at time \(t\) seconds.
Find, in vector form, an expression for the force acting on the object at time \(t\) seconds.