4 A car of mass 1200 kg is moving on a straight road against a constant force of 850 N resisting the motion.
- On a part of the road that is horizontal, the car moves with a constant speed of \(42 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
(a) Calculate, in kW , the power developed by the engine of the car.
(b) Given that this power is suddenly increased by 6 kW , find the instantaneous acceleration of the car. - On a part of the road that is inclined at \(\theta ^ { \circ }\) to the horizontal, the car moves up the hill at a constant speed of \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), with the engine working at 80 kW . Find \(\theta\).
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A particle of mass 0.12 kg is placed on a plane which is inclined at an angle of \(40 ^ { \circ }\) to the horizontal. The particle is kept in equilibrium by a force of magnitude \(P \mathrm {~N}\) acting up the plane at an angle of \(30 ^ { \circ }\) above a line of greatest slope, as shown in the diagram. The coefficient of friction between the particle and the plane is 0.32 . Find the set of possible values of \(P\).