1 A bus of mass 8 tonnes is driven up a hill on a straight road. On one part of the hill, the power of the driving force on the bus is constant at 20 kW for one minute.

1. Calculate how much work is done by the driving force in this time. During this minute the speed of the bus increases from \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(12 \mathrm {~ms} ^ { - 1 }\) and, in addition to the work done against gravity, 125000 J of work is done against the resistance to motion of the bus parallel to the slope.
2. Calculate the change in the kinetic energy of the bus.
3. Calculate the vertical displacement of the bus. On another stretch of the road, a driving force of power 26 kW is required to propel the bus up a slope of angle \(\theta\) to the horizontal at a constant speed of \(6.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), against a resistance to motion of 225 N parallel to the slope.
4. Calculate the angle \(\theta\). The bus later travels up the same slope of angle \(\theta\) to the horizontal at the same constant speed of \(6.5 \mathrm {~ms} ^ { - 1 }\) but now against a resistance to motion of 155 N parallel to the slope.
5. Calculate the power of the driving force on the bus.