| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Engine power on road constant/variable speed |
| Difficulty | Moderate -0.3 This is a straightforward M2 power-resistance question requiring standard formulas (P=Fv, work-energy principle). Part (i) is direct substitution; part (ii) uses work-energy theorem with given values. Both parts follow textbook methods with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(D = 480/v\) | B1 | Use of \(D = P/v\) |
| \(480/v - 60 = 0\) | M1 | Use of N2L with 2 terms to find \(v\) |
| \(v = 8 \text{ m s}^{-1}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(600 \times 14.2\) | B1 | WD by cyclist (8520 J) |
| \(\frac{1}{2}(80)(9.4^2 - 8^2)\) | B1ft | ft \(v\) from (i); KE gained (974.4 J); may be implied in energy equation |
| \(8520 = 974.4 + 60d\) | M1 | Attempt at energy equation with all terms |
| \(d = 126 \text{ m}\) | A1 | Exact 125.76 |
## Question 1:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $D = 480/v$ | B1 | Use of $D = P/v$ |
| $480/v - 60 = 0$ | M1 | Use of N2L with 2 terms to find $v$ |
| $v = 8 \text{ m s}^{-1}$ | A1 | |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $600 \times 14.2$ | B1 | WD by cyclist (8520 J) |
| $\frac{1}{2}(80)(9.4^2 - 8^2)$ | B1ft | ft $v$ from (i); KE gained (974.4 J); may be implied in energy equation |
| $8520 = 974.4 + 60d$ | M1 | Attempt at energy equation with all terms |
| $d = 126 \text{ m}$ | A1 | Exact 125.76 |
---1 A cyclist travels along a straight horizontal road. The total mass of the cyclist and her bicycle is 80 kg and the resistance to motion is a constant 60 N .\\
(i) The cyclist travels at a constant speed working at a constant rate of 480 W . Find the speed at which she travels.\\
(ii) The cyclist now instantaneously increases her power to 600 W . After travelling at this power for 14.2 s her speed reaches $9.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find the distance travelled at this power.
\hfill \mbox{\textit{OCR M2 2015 Q1 [7]}}