6. Two cars \(A\) and \(B\) are moving in the same direction along a straight horizontal road. At time \(t = 0\), they are side by side, passing a point \(O\) on the road. Car \(A\) travels at a constant speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Car \(B\) passes \(O\) with a speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and has constant acceleration of \(4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Find

1. the speed of \(B\) when it has travelled 78 m from \(O\),
2. the distance from \(O\) of \(A\) when \(B\) is 78 m from \(O\),
3. the time when \(B\) overtakes \(A\).
   (5) \section*{7.} \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{31c17a67-4fcf-4402-b00e-239ce9f20964-5_271_926_392_639}
   \end{figure} A sledge has mass 30 kg . The sledge is pulled in a straight line along horizontal ground by means of a rope. The rope makes an angle \(20 ^ { \circ }\) with the horizontal, as shown in Figure 3. The coefficient of friction between the sledge and the ground is 0.2 . The sledge is modelled as a particle and the rope as a light inextensible string. The tension in the rope is 150 N . Find, to 3 significant figures,
4. the normal reaction of the ground on the sledge,
5. the acceleration of the sledge. When the sledge is moving at \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the rope is released from the sledge.
6. Find, to 3 significant figures, the distance travelled by the sledge from the moment when the rope is released to the moment when the sledge comes to rest.
   (6) \section*{8.} \section*{Figure 4}
   \includegraphics[max width=\textwidth, alt={}]{31c17a67-4fcf-4402-b00e-239ce9f20964-6_513_570_340_753}
   A heavy package is held in equilibrium on a slope by a rope. The package is attached to one end of the rope, the other end being held by a man standing at the top of the slope. The package is modelled as a particle of mass 20 kg . The slope is modelled as a rough plane inclined at \(60 ^ { \circ }\) to the horizontal and the rope as a light inextensible string. The string is assumed to be parallel to a line of greatest slope of the plane, as shown in Figure 4. At the contact between the package and the slope, the coefficient of friction is 0.4 .
7. Find the minimum tension in the rope for the package to stay in equilibrium on the slope.
   (8) The man now pulls the package up the slope. Given that the package moves at constant speed,
8. find the tension in the rope.
9. State how you have used, in your answer to part (b), the fact that the package moves
   1. up the slope,
   2. at constant speed.