| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | March |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find steady/maximum speed given power |
| Difficulty | Moderate -0.5 This is a straightforward application of the power formula P = Fv. Part (i) requires recognizing that at constant speed, driving force equals resistance, then calculating power. Part (ii) involves resolving forces on an incline and solving for speed. Both parts use standard mechanics techniques with no conceptual challenges—slightly easier than average due to the direct application of formulas and clear problem structure. |
| Spec | 6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(DF = 1350\) | B1 | |
| \(P = 1350 \times 32 = 43.2\) kW | B1 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(DF - 1350 - 1200g \times 0.1 = 0 \Rightarrow [DF = 2550]\) | M1 | For using Newton's 2nd law applied to the car up the hill (3 terms); allow use of \(\theta = 5.7°\) |
| \(DF = 76500/v\) | M1 | For using \(DF = P/v\) |
| \(v = 30\ \text{ms}^{-1}\) | A1 | 3 |
## Question 2:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $DF = 1350$ | B1 | |
| $P = 1350 \times 32 = 43.2$ kW | B1 | 2 | |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $DF - 1350 - 1200g \times 0.1 = 0 \Rightarrow [DF = 2550]$ | M1 | For using Newton's 2nd law applied to the car up the hill (3 terms); allow use of $\theta = 5.7°$ |
| $DF = 76500/v$ | M1 | For using $DF = P/v$ |
| $v = 30\ \text{ms}^{-1}$ | A1 | 3 | |
---2 A constant resistance of magnitude 1350 N acts on a car of mass 1200 kg .\\
(i) The car is moving along a straight level road at a constant speed of $32 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find, in kW , the rate at which the engine of the car is working.\\
(ii) The car travels at a constant speed up a hill inclined at an angle of $\theta$ to the horizontal, where $\sin \theta = 0.1$, with the engine working at 76.5 kW . Find this speed.
\hfill \mbox{\textit{CAIE M1 2016 Q2 [5]}}