1. A racing car starts from rest at the point \(A\) and moves with constant acceleration.of \(11 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 8 s . The velocity it has reached after 8 s is then maintained for \(T \mathrm {~s}\). The racing car then decelerates from this velocity to \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a further 2 s , reaching point \(B\).
   a Sketch a velocity-time graph to illustrate the motion of the racing car. Include the top speed of the racing car in your sketch.
   b Given that the distance between \(A\) and \(B\) is 1404 m , find the value of \(T\).
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2. A particle \(P\) is acted upon by three forces \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\) given by \(\mathbf { F } _ { 1 } = ( 6 \mathbf { i } - 4 \mathbf { j } ) \mathrm { N } , \mathbf { F } _ { 2 } = ( - 2 \mathbf { i } + 9 \mathbf { j } ) \mathrm { N }\) and \(\mathbf { F } _ { 3 } = ( a \mathbf { i } + b \mathbf { j } ) \mathrm { N }\), where \(a\) and \(b\) are constants. Given that \(P\) is in equilibrium,
   a find the value of \(a\) and the value of \(b\).

The force \(\mathbf { F } _ { 2 }\) is now removed. The resultant of \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 3 }\) is \(\mathbf { R }\).
b Find the magnitude of \(\mathbf { R }\).
c Find the angle, to \(0.1 ^ { \circ }\), that \(\mathbf { R }\) makes with \(\mathbf { i }\).
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