A car of mass 1250 kg travels along a horizontal straight road. The power of the car’s engine is constant and equal to 24 kW and the resistance to the car’s motion is constant and equal to \(R\) N. The car passes through the point \(A\) on the road with speed 20 m/s and acceleration 0.32 m/s².

1. Find the value of \(R\).

The car continues with increasing speed, passing through the point \(B\) on the road with speed 29.9 m/s. The car subsequently passes through the point \(C\).

2. Find the acceleration of the car at \(B\), giving the answer in m/s² correct to 3 decimal places.
3. Show that, while the car’s speed is increasing, it cannot reach 30 m/s.
4. Explain why the speed of the car is approximately constant between \(B\) and \(C\).
5. State a value of the approximately constant speed, and the maximum possible error in this value at any point between \(B\) and \(C\).

The work done by the car’s engine during the motion from \(B\) to \(C\) is 1200 kJ.

6. By assuming the speed of the car is constant from \(B\) to \(C\), find, in either order,
   1. the approximate time taken for the car to travel from \(B\) to \(C\),
   2. an approximation for the distance \(BC\).