| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Engine power on road constant/variable speed |
| Difficulty | Standard +0.3 This is a straightforward application of the work-energy principle and power formula (P = Fv). Part (i) uses work done = change in KE with constant power, requiring simple algebra. Part (ii) applies P = Fv then F = ma. Both parts are standard M2 techniques with no resistance forces to complicate the problem, making it slightly easier than average. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(WD = \frac{1}{2}\times250\times150^2 - \frac{1}{2}\times250\times100^2\) | M1 | |
| \(1\,560\,000\) | A1 | \(1\,562\,500\) |
| \(450\,000 = 1\,560\,000/t\) | M1 | |
| \(3.47\) | A1 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(F = 450\,000/120\) | M1 | |
| \(3750\) | A1 | |
| \(3750 = 250a\) | M1 | |
| \(15\ \text{ms}^{-2}\) | A1 4 |
## Question 3(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $WD = \frac{1}{2}\times250\times150^2 - \frac{1}{2}\times250\times100^2$ | M1 | |
| $1\,560\,000$ | A1 | $1\,562\,500$ |
| $450\,000 = 1\,560\,000/t$ | M1 | |
| $3.47$ | A1 **4** | |
## Question 3(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $F = 450\,000/120$ | M1 | |
| $3750$ | A1 | |
| $3750 = 250a$ | M1 | |
| $15\ \text{ms}^{-2}$ | A1 **4** | |
---3 A rocket of mass 250 kg is moving in a straight line in space. There is no resistance to motion, and the mass of the rocket is assumed to be constant. With its motor working at a constant rate of 450 kW the rocket's speed increases from $100 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ to $150 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in a time $t$ seconds.\\
(i) Calculate the value of $t$.\\
(ii) Calculate the acceleration of the rocket at the instant when its speed is $120 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\hfill \mbox{\textit{OCR M2 2007 Q3 [8]}}