1. A lorry has mass 5000 kg .

In all circumstances, when the speed of the lorry is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the resistance to motion of the lorry from non-gravitational forces is modelled as having magnitude \(490 v\) newtons. The lorry moves along a straight horizontal road at \(12 \mathrm {~ms} ^ { - 1 }\), with its engine working at a constant rate of 84 kW . Using the model,

1. find the acceleration of the lorry. Another straight road is inclined to the horizontal at an angle \(\alpha\) where \(\sin \alpha = \frac { 1 } { 14 }\)
   With its engine again working at a constant rate of 84 kW , the lorry can maintain a constant speed of \(V \mathrm {~ms} ^ { - 1 }\) up the road. Using the model,
2. find the value of \(V\).