M2 June 2005 Q1
1. A car of mass 1200 kg moves along a straight horizontal road. The resistance to motion of the car from non-gravitational forces is of constant magnitude 600 N. The car moves with constant speed and the engine of the car is working at a rate of 21 kW.
(a) Find the speed of the car. (3)
The car moves up a hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin\alpha = \tfrac{1}{14}\). The car’s engine continues to work at 21 kW, and the resistance to motion from non-gravitational forces remains of magnitude 600 N.
(b) Find the constant speed at which the car can move up the hill. (4)
| Scheme | Marks |
|---|---|
| Driving force \(= \dfrac{P}{v}\) | B1 |
| \(\dfrac{21000}{v} = 600\ \Rightarrow\ v = 35\) m s\(^{-1}\) | M1 A1 |
| (3) |
| Scheme | Marks |
|---|---|
| \(\dfrac{P}{v} = 600 + 1200.g.\dfrac{1}{14}\) | M1 A1 |
| \((= 1440\ \text{N})\) | |
| \(\dfrac{21000}{v} = 1440 \Rightarrow v = \dfrac{21000}{1440} \approx 14.6\) or 15 m s\(^{-1}\) | M1 A1 |
| (4) | |
| (7 marks) |