AS June 2023 Q2

2. A racing car of mass 750 kg is moving along a straight horizontal road at a constant speed of \(U\) km h⁻¹. The engine of the racing car is working at a constant rate of 60 kW.

The resistance to the motion of the racing car is modelled as a force of magnitude \(37.5v\) N, where \(v\ \text{m s}^{-1}\) is the speed of the racing car.

Using the model,

Later on, the racing car is accelerating up a straight road which is inclined to the horizontal at an angle \(\alpha\), where \(\sin\alpha = \dfrac{5}{49}\). The engine of the racing car is working at a constant rate of 60 kW.

The total resistance to the motion of the racing car from non-gravitational forces is modelled as a force of magnitude \(37.5v\) N, where \(v\ \text{m s}^{-1}\) is the speed of the racing car.
At the instant when the acceleration of the racing car is \(2\ \text{m s}^{-2}\), the speed of the racing car is \(V\ \text{m s}^{-1}\)

Using the model,