A particle of mass 0.8 kg is moving in a straight line on a rough horizontal plane. The speed of the particle is reduced from \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) as the particle moves 20 m . Assuming that the only resistance to motion is the friction between the particle and the plane, find
the work done by friction in reducing the speed of the particle from \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\),
the coefficient of friction between the particle and the plane.
A car of mass 800 kg is moving at a constant speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) down a straight road inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 24 }\). The resistance to motion from non-gravitational forces is modelled as a constant force of magnitude 900 N .
Find, in kW , the rate of working of the engine of the car.
When the car is travelling down the road at \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the engine is switched off. The car comes to rest in time \(T\) seconds after the engine is switched off. The resistance to motion from non-gravitational forces is again modelled as a constant force of magnitude 900 N .