5 A particle \(P\) moves along a straight line in such a way that at time \(t\) seconds \(P\) has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where
$$v = 12 \cos t + 5 \sin t .$$
- Express \(v\) in the form \(R \cos ( t - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\). Give the value of \(\alpha\) correct to \(\mathbf { 4 }\) significant figures.
- Hence find the two smallest positive values of \(t\) for which \(P\) is moving, in either direction, with a speed of \(3 \mathrm {~ms} ^ { - 1 }\).