2.
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\caption{Figure 2}
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A truck of mass 1200 kg is being driven up a straight road that is inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 15 }\). The resistance to the motion of the truck from non-gravitational forces is modelled as a single constant force of magnitude 250 N . Two points, \(A\) and \(B\), lie on the road, with \(A B = 90 \mathrm {~m}\). The speed of the truck at \(A\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of the truck at \(B\) is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), as shown in Figure 2.
The truck is modelled as a particle and the road is modelled as a straight line.
- Find the work done by the engine of the truck as the truck moves from \(A\) to \(B\).
On another occasion, the truck is being driven down the same road. The resistance to the motion of the truck is modelled as a single constant force of magnitude 250 N . The engine of the truck is working at a constant rate of 8 kW .
- Find the acceleration of the truck at the instant when its speed is \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).