1 A car of mass 1400 kg is travelling on a straight horizontal road against a constant resistance to motion of 600 N . At a certain instant the car is accelerating at \(0.3 \mathrm {~ms} ^ { - 2 }\) and the engine of the car is working at a rate of 23 kW .

1. Find the speed of the car at this instant. Subsequently the car moves up a hill inclined at \(10 ^ { \circ }\) to the horizontal at a steady speed of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The resistance to motion is still a constant 600 N .
2. Calculate the power of the car's engine as it moves up the hill.
   \(2 A\) and \(B\) are two points on a line of greatest slope of a plane inclined at \(55 ^ { \circ }\) to the horizontal. \(A\) is below the level of \(B\) and \(A B = 4 \mathrm {~m}\). A particle \(P\) of mass 2.5 kg is projected up the plane from \(A\) towards \(B\) and the speed of \(P\) at \(B\) is \(6.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The coefficient of friction between the plane and \(P\) is 0.15 . Find
3. the work done against the frictional force as \(P\) moves from \(A\) to \(B\),
4. the initial speed of \(P\) at \(A\).