| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find acceleration on incline given power |
| Difficulty | Moderate -0.3 This is a straightforward application of the power-force-velocity relationship (P = Fv) combined with Newton's second law. Part (i) requires simple substitution into standard formulas, while part (ii) adds an incline component but remains routine. The zero resistance simplifies calculations, and both parts follow standard M1 procedures without requiring problem-solving insight. |
| Spec | 6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(\frac{P}{5} = 80 \times 1.2\) | M1 | For using \(DF = \frac{P}{v}\) and Newton's 2nd law |
| \(P = 480\) | A1 | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(\frac{450}{3.6} - 80g \times 0.035 = 80a\) | M1, A1 | For using \(\frac{P}{v} - W\sin\alpha = ma\) |
| Acceleration is \(1.21\) ms\(^{-2}\) | A1 | [3] Allow \(a = \frac{97}{80}\) |
## Question 2:
### Part (i)
| Working/Answer | Mark | Guidance |
|---|---|---|
| $\frac{P}{5} = 80 \times 1.2$ | M1 | For using $DF = \frac{P}{v}$ and Newton's 2nd law |
| $P = 480$ | A1 | **[2]** |
### Part (ii)
| Working/Answer | Mark | Guidance |
|---|---|---|
| $\frac{450}{3.6} - 80g \times 0.035 = 80a$ | M1, A1 | For using $\frac{P}{v} - W\sin\alpha = ma$ |
| Acceleration is $1.21$ ms$^{-2}$ | A1 | **[3]** Allow $a = \frac{97}{80}$ |
---2 The total mass of a cyclist and his cycle is 80 kg . The resistance to motion is zero.\\
(i) The cyclist moves along a horizontal straight road working at a constant rate of $P \mathrm {~W}$. Find the value of $P$ given that the cyclist's speed is $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ when his acceleration is $1.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
(ii) The cyclist moves up a straight hill inclined at an angle $\alpha$, where $\sin \alpha = 0.035$. Find the acceleration of the cyclist at an instant when he is working at a rate of 450 W and has speed $3.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\hfill \mbox{\textit{CAIE M1 2015 Q2 [5]}}