M2 June 2006 Q2
2. A car of mass 1200 kg moves along a straight horizontal road with a constant speed of 24 m s\(^{-1}\). The resistance to motion of the car has magnitude 600 N.
(a) Find, in kW, the rate at which the engine of the car is working. (2)
The car now moves up a hill inclined at \(\alpha\) to the horizontal, where \(\sin\alpha = \tfrac{1}{28}\). The resistance to motion of the car from non-gravitational forces remains of magnitude 600 N. The engine of the car now works at a rate of 30 kW.
(b) Find the acceleration of the car when its speed is 20 m s\(^{-1}\). (4)
| Scheme | Marks |
|---|---|
| \(\dfrac{P}{24} = 600\) or \(\dfrac{1000P}{24} = 600\ \ \Rightarrow\ \ P = 14.4\,kW\) | M1 A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(\dfrac{30000}{20} - 1200 \times 9.8 \times \sin\alpha - 600 = 1200a\) | M1 A2,1,0 |
| \(\Rightarrow a = \underline{0.4\ \text{m s}^{-2}}\) | A1 |
| (4) | |
| (6 marks) |