| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Cyclist or runner: find resistance or speed |
| Difficulty | Moderate -0.3 This is a straightforward application of the power-force-velocity relationship (P = Fv) combined with Newton's second law. Part (i) requires substituting given values into standard formulas, while part (ii) involves a simple inequality derived from the condition that acceleration is positive. Both parts are routine M1 mechanics with no novel problem-solving required. |
| Spec | 3.03d Newton's second law: 2D vectors6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = 720/12\) | B1 | |
| \([F - R = 75 \times 0.16]\) | M1 | For use of Newton's second law |
| \(R = 48\) | A1 | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| \([720/v > 48]\) | M1 | For using \(P/v - R = ma\) and \(a > 0 \Rightarrow P/v > R\) |
| \(v < 15\) i.e. speed is less than \(15 \text{ m s}^{-1}\) | A1 | 2 |
**(i)**
$F = 720/12$ | B1 |
$[F - R = 75 \times 0.16]$ | M1 | For use of Newton's second law
$R = 48$ | A1 | 3
**(ii)**
$[720/v > 48]$ | M1 | For using $P/v - R = ma$ and $a > 0 \Rightarrow P/v > R$
$v < 15$ i.e. speed is less than $15 \text{ m s}^{-1}$ | A1 | 2
---1 A racing cyclist, whose mass with his cycle is 75 kg , works at a rate of 720 W while moving on a straight horizontal road. The resistance to the cyclist's motion is constant and equal to $R \mathrm {~N}$.\\
(i) Given that the cyclist is accelerating at $0.16 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ at an instant when his speed is $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, find the value of $R$.\\
(ii) Given that the cyclist's acceleration is positive, show that his speed is less than $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\hfill \mbox{\textit{CAIE M1 2011 Q1 [5]}}