7 A car has mass 1200 kg . When the car is travelling at a speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), there is a resistive force of magnitude \(k v \mathrm {~N}\). The maximum power of the car's engine is 92.16 kW .

1. The car travels along a straight level road.
   1. The car has a greatest possible constant speed of \(48 \mathrm {~ms} ^ { - 1 }\). Show that \(k = 40\).
   2. At an instant when its speed is \(45 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), find the greatest possible acceleration of the car. [3]
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2. The car now travels at a constant speed up a hill inclined at an angle of \(\sin ^ { - 1 } 0.15\) to the horizontal. Find the greatest possible speed of the car going up the hill.