2. A van of mass 1500 kg is driving up a straight road inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 12 }\). The resistance to motion due to non-gravitational forces is modelled as a constant force of magnitude 1000 N .
Given that initially the speed of the van is \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and that the van's engine is working at a rate of 60 kW ,
- calculate the magnitude of the initial decleration of the van.
When travelling up the same hill, the rate of working of the van's engine is increased to 80 kW . Using the same model for the resistance due to nongravitational forces,
- calculate in \(\mathrm { m } \mathrm { s } ^ { - 1 }\) the constant speed which can be sustained by the van at this rate of working.
- Give one reason why the use of this model for resistance may mean that your answer to part (b) is too high.