| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Constant power on horizontal road |
| Difficulty | Standard +0.3 This is a straightforward application of the power-force-velocity relationship (P = Fv) with constant resistance. Part (i) requires recognizing that maximum speed occurs when driving force equals resistance, a standard textbook scenario. Part (ii) involves using F = ma after finding the driving force from P/v. Both parts are routine mechanics calculations with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| Part (i) | ||
| \([DF = 600 \text{ at max speed}]\) | M1 | For using DF = R at max. speed |
| \([DF = \frac{24000}{v}]\) | M1 | For using DF = P/v |
| Speed cannot exceed 40 m s\(^{-1}\) | A1 | 3 |
| Part (ii) | ||
| \([DF - R = ma]\) | M1 | For using Newton's second law |
| \(\frac{24000}{15} - 600 = 1250a\) | A1 | |
| Acceleration is 0.8 m s\(^{-2}\) | A1 | 3 |
| **Part (i)** | | |
|---|---|---|
| $[DF = 600 \text{ at max speed}]$ | M1 | For using DF = R at max. speed |
| $[DF = \frac{24000}{v}]$ | M1 | For using DF = P/v |
| Speed cannot exceed 40 m s$^{-1}$ | A1 | 3 | AG |
| **Part (ii)** | | |
|---|---|---|
| $[DF - R = ma]$ | M1 | For using Newton's second law |
| $\frac{24000}{15} - 600 = 1250a$ | A1 | |
| Acceleration is 0.8 m s$^{-2}$ | A1 | 3 |3 A car of mass 1250 kg travels along a horizontal straight road with increasing speed. The power provided by the car's engine is constant and equal to 24 kW . The resistance to the car's motion is constant and equal to 600 N .\\
(i) Show that the speed of the car cannot exceed $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(ii) Find the acceleration of the car at an instant when its speed is $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\hfill \mbox{\textit{CAIE M1 2009 Q3 [6]}}