| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find steady/maximum speed given power |
| Difficulty | Moderate -0.5 This is a straightforward application of the power-force-velocity relationship (P=Fv) at maximum speed where acceleration is zero, followed by Newton's second law. Both parts require direct substitution into standard formulas with minimal problem-solving insight needed. |
| Spec | 3.03c Newton's second law: F=ma one dimension6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \([DF = 18000/30]\) | M1 | For using \(DF = P/v\) — may be scored in (ii) |
| \([R = DF]\) | M1 | For using \(a = 0\) (may be implied) |
| \(R = 600\ \text{N}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| M1 | For using Newton's second law (3 terms) | |
| \(18000/20 - 600 = 1200a\) | A1ft | ft wrong \(R\) |
| Acceleration is \(0.25\ \text{ms}^{-2}\) | A1 |
## Question 3:
### Part (i):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $[DF = 18000/30]$ | M1 | For using $DF = P/v$ — may be scored in (ii) |
| $[R = DF]$ | M1 | For using $a = 0$ (may be implied) |
| $R = 600\ \text{N}$ | A1 | |
### Part (ii):
| Working/Answer | Mark | Guidance |
|---|---|---|
| | M1 | For using Newton's second law (3 terms) |
| $18000/20 - 600 = 1200a$ | A1ft | ft wrong $R$ |
| Acceleration is $0.25\ \text{ms}^{-2}$ | A1 | |
---3 A car travels along a horizontal straight road with increasing speed until it reaches its maximum speed of $30 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The resistance to motion is constant and equal to $R \mathrm {~N}$, and the power provided by the car's engine is 18 kW .\\
(i) Find the value of $R$.\\
(ii) Given that the car has mass 1200 kg , find its acceleration at the instant when its speed is $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\hfill \mbox{\textit{CAIE M1 2007 Q3 [6]}}