5. A lorry of mass 40 tonnes moves up a straight road inclined at an angle \(\alpha\) to the horizontal where \(\sin \alpha = \frac { 1 } { 20 }\). The lorry moves at a constant speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In a model of the motion of the lorry, the non-gravitational resistance to motion is assumed to be constant and of magnitude 4400 N .

1. Show that the engine of the lorry is working at a rate of 480 kW . The road becomes horizontal. The lorry's engine continues to work at the same rate and the resistance to motion is assumed to remain unchanged.
2. Find the initial acceleration of the lorry.
3. Find, correct to 3 significant figures, the maximum speed of the lorry.
4. Using your answer to part (c), comment on the suitability of the modelling assumption.