Standard +0.3 This is a straightforward application of the power-force-velocity relationship (P = Fv) combined with Newton's second law on an incline. Students must resolve forces parallel to the slope, apply F = ma to find the driving force, then use P = Fv to find velocity. It requires multiple standard steps but no novel insight—slightly easier than average due to being a direct application of well-practiced techniques.
2 A car of mass 1250 kg travels up a straight hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.02\). The power provided by the car's engine is 23 kW . The resistance to motion is constant and equal to 600 N . Find the speed of the car at an instant when its acceleration is \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
For using WD by driving force \(= DF \times s\) and \(DF = 23000/v\)
\(v = 23000 \div (625 + 600 + 250)\)
A1ft
ft error in one term for WD above (1st A mark)
Speed of car is \(15.6\ \text{ms}^{-1}\)
A1 [5]
## Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For using Newton's 2nd law |
| $DF - 600 - 1250 \times 0.02g = 1250 \times 0.5$ | A1 | |
| | M1 | For using $DF = 23000/v$ |
| $v = 23000 \div (625 + 600 + 250)$ | A1ft | ft error in one term for DF above (1st A mark) |
| Speed of car is $15.6\ \text{ms}^{-1}$ | A1 [5] | |
**Alternative Method:**
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For using WD by driving force $=$ KE gain $+$ PE gain $+$ WD against resistance |
| $WD = 1250 \times 0.5s + 1250g \times 0.02s + 600s$ | A1 | |
| | M1 | For using WD by driving force $= DF \times s$ and $DF = 23000/v$ |
| $v = 23000 \div (625 + 600 + 250)$ | A1ft | ft error in one term for WD above (1st A mark) |
| Speed of car is $15.6\ \text{ms}^{-1}$ | A1 [5] | |
---
2 A car of mass 1250 kg travels up a straight hill inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = 0.02$. The power provided by the car's engine is 23 kW . The resistance to motion is constant and equal to 600 N . Find the speed of the car at an instant when its acceleration is $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\hfill \mbox{\textit{CAIE M1 2014 Q2 [5]}}