- A car of mass 1000 kg moves in a straight line along a horizontal road at a constant speed of \(72 \mathrm {~km} \mathrm {~h} ^ { - 1 }\)
- The resistance to the motion of the car is modelled as a constant force of magnitude 900 N
The engine of the car is working at a constant rate of \(P \mathrm {~kW}\).
Using the model,
- find the value of \(P\).
The car now travels in a straight line up a road which is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 2 } { 49 }\)
- In a refined model, the resistance to the motion of the car from non-gravitational forces is now modelled as a force of magnitude \(20 v\) newtons, where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the speed of the car
At the instant when the engine of the car is working at a constant rate of 30 kW and the car is moving up the road at \(10 \mathrm {~ms} ^ { - 1 }\), the acceleration of the car is \(a \mathrm {~ms} ^ { - 2 }\)
Using the refined model, - find the value of \(a\).
Later on, when the engine of the car is again working at a constant rate of 30 kW , the car is moving up the road at a constant speed \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
Using the refined model,
- find the value of \(U\).