3 A car of mass 1400 kg is travelling up a hill inclined at an angle of \(4 ^ { \circ }\) to the horizontal. There is a constant resistance to motion of magnitude 1550 N acting on the car.
- Given that the engine of the car is working at 30 kW , find the speed of the car at an instant when its acceleration is \(0.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- The greatest possible constant speed at which the car can travel up the hill is \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the maximum possible power of the engine.
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Two particles \(A\) and \(B\), of masses 1.3 kg and 0.7 kg respectively, are connected by a light inextensible string which passes over a smooth fixed pulley. Particle \(A\) is 1.75 m above the floor and particle \(B\) is 1 m above the floor (see diagram). The system is released from rest with the string taut, and the particles move vertically. When the particles are at the same height the string breaks.