| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Vehicle on slope with resistance |
| Difficulty | Moderate -0.3 This is a straightforward mechanics problem requiring Newton's second law on an inclined plane with given resistance. Part (i) involves resolving forces and substituting known values into F = ma. Part (ii) uses standard kinematics (v² = u² + 2as). Both parts are routine applications of standard M1 techniques with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03d Newton's second law: 2D vectors6.02a Work done: concept and definition |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For applying Newton's 2nd law to the bicycle/cyclist | |
| \(F - 780 \times (36 \div 325) - 32 = 78 \times (-0.2)\) | A2 | A2 for all correct, A1 for one error, A0 for more than one error |
| \(F = 103\) (\(102.8\) exact) | A1 [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(0 = 7^2 + 2(-0.2)s\) | M1 | For using \(0 = u^2 + 2as\) |
| Distance is \(122.5\) m (accept 122 or 123) | A1 [2] |
## Question 3:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For applying Newton's 2nd law to the bicycle/cyclist |
| $F - 780 \times (36 \div 325) - 32 = 78 \times (-0.2)$ | A2 | A2 for all correct, A1 for one error, A0 for more than one error |
| $F = 103$ ($102.8$ exact) | A1 [4] | |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $0 = 7^2 + 2(-0.2)s$ | M1 | For using $0 = u^2 + 2as$ |
| Distance is $122.5$ m (accept 122 or 123) | A1 [2] | |
---3 A cyclist exerts a constant driving force of magnitude $F \mathrm {~N}$ while moving up a straight hill inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 36 } { 325 }$. A constant resistance to motion of 32 N acts on the cyclist. The total weight of the cyclist and his bicycle is 780 N . The cyclist's acceleration is $- 0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
(i) Find the value of $F$.
The cyclist's speed is $7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at the bottom of the hill.\\
(ii) Find how far up the hill the cyclist travels before coming to rest.
\hfill \mbox{\textit{CAIE M1 2013 Q3 [6]}}