1. A car is initially travelling with a constant velocity of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for \(T \mathrm {~s}\). It then decelerates at a constant rate for \(\frac { T } { 2 } \mathrm {~s}\), reaching a velocity of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It then immediately accelerates at a constant rate for \(\frac { 3 T } { 2 } \mathrm {~s}\) reaching a velocity of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
   a Sketch a velocity-time graph to illustrate the motion.
   b Given that the car travels a total distance of 1312.5 m over the journey described, find the value of \(T\).
   [0pt] [BLANK PAGE]
2. A particle \(P\) moves in a straight line. At time \(t \mathrm {~s}\) the displacement \(s \mathrm {~cm}\) from a fixed point \(O\) is given by: \(s = \frac { 1 } { 6 } \left( 8 t ^ { 3 } - 105 t ^ { 2 } + 144 t + 540 \right)\).
   Find the distance between the points at which the particle is instantaneously at rest.
   [0pt] [BLANK PAGE]
3. A cylindrical object with mass 8 kg rests on two cylindrical bars of equal radius. The lines connecting the centre of each of the bars to the centre of the object make an angle of \(40 ^ { \circ }\) to the vertical.

\begin{figure}[h] \end{figure} a Draw a diagram showing all the forces acting on the object. Describe each of the forces using words.
b Calculate the magnitude of the force on each of the bars due to the cylindrical object.
[0pt] [BLANK PAGE]