| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2019 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Cyclist or runner: find resistance or speed |
| Difficulty | Moderate -0.3 This is a straightforward multi-part mechanics question requiring standard application of P=Fv and F=ma with constant resistance. Part (i) uses Newton's second law with power equation, part (ii) finds steady speed (zero acceleration), and part (iii) adds an incline component. All steps are routine M1 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Driving force \(= \frac{240}{6}\) \((= 40\text{ N})\) | B1 | Use of power \(=\) force \(\times\) velocity |
| \([40 - R = 80\times0.3]\) | M1 | Use of Newton's Second Law (3 terms) |
| Resistance is \(16\) N | A1 | AG |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\left[\frac{240}{v} = 16\right]\) | M1 | Use of \(P=Fv\) with DF \(=\) resistance |
| Steady speed is \(15 \text{ ms}^{-1}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Use of Newton's Second Law | M1 | (4 terms) |
| \(\frac{240}{4} - 16 - 80g\sin3 = 80a\) | A1 | |
| Acceleration is \(0.0266 \text{ ms}^{-2}\) | A1 |
## Question 5(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Driving force $= \frac{240}{6}$ $(= 40\text{ N})$ | B1 | Use of power $=$ force $\times$ velocity |
| $[40 - R = 80\times0.3]$ | M1 | Use of Newton's Second Law (3 terms) |
| Resistance is $16$ N | A1 | AG |
## Question 5(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\left[\frac{240}{v} = 16\right]$ | M1 | Use of $P=Fv$ with DF $=$ resistance |
| Steady speed is $15 \text{ ms}^{-1}$ | A1 | |
## Question 5(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Use of Newton's Second Law | M1 | (4 terms) |
| $\frac{240}{4} - 16 - 80g\sin3 = 80a$ | A1 | |
| Acceleration is $0.0266 \text{ ms}^{-2}$ | A1 | |5 A cyclist is travelling along a straight horizontal road. The total mass of the cyclist and his bicycle is 80 kg . His power output is a constant 240 W . His acceleration when he is travelling at $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is $0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
(i) Show that the resistance to the cyclist's motion is 16 N .\\
(ii) Find the steady speed that the cyclist can maintain if his power output and the resistance force are both unchanged.\\
(iii) The cyclist later ascends a straight hill inclined at $3 ^ { \circ }$ to the horizontal. His power output and the resistance force are still both unchanged. Find his acceleration when he is travelling at $4 \mathrm {~ms} ^ { - 1 }$.\\
\hfill \mbox{\textit{CAIE M1 2019 Q5 [8]}}