1. A van of mass 750 kg is moving along a straight horizontal road. At the instant when the van is moving at \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the resistance to the motion of the van is modelled as a force of magnitude \(\lambda \nu \mathrm { N }\), where \(\lambda\) is a constant.

The engine of the van is working at a constant rate of 18 kW .
At the instant when \(v = 15\), the acceleration of the van is \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)

1. Show that \(\lambda = 50\) The van now moves up a straight road inclined at an angle to the horizontal, where \(\sin \alpha = \frac { 1 } { 15 }\)
   At the instant when the van is moving at \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the resistance to the motion of the van from non-gravitational forces is modelled as a force of magnitude 50 v . When the engine of the van is working at a constant rate of 12 kW , the van is moving at a constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
2. Find the value of \(V\).

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