Three posts \(P , Q\) and \(R\), are fixed in that order at the side of a straight horizontal road. The distance from \(P\) to \(Q\) is 45 m and the distance from \(Q\) to \(R\) is 120 m . A car is moving along the road with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The speed of the car, as it passes \(P\), is \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car passes \(Q\) two seconds after passing \(P\), and the car passes \(R\) four seconds after passing \(Q\). Find
the value of \(u\),
the value of \(a\).
A particle is acted upon by two forces \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\), given by
\(\mathbf { F } _ { 1 } = ( \mathbf { i } - 3 \mathbf { j } ) \mathrm { N }\),
\(\mathbf { F } _ { 2 } = ( p \mathbf { i } + 2 p \mathbf { j } ) \mathrm { N }\), where \(p\) is a positive constant.
(a) Find the angle between \(\mathbf { F } _ { 2 }\) and \(\mathbf { j }\).
The resultant of \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\) is \(\mathbf { R }\). Given that \(\mathbf { R }\) is parallel to \(\mathbf { i }\),
(b) find the value of \(p\).