| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Variable power or two power scenarios |
| Difficulty | Moderate -0.3 This is a straightforward application of P=Fv and F=ma with constant power. Part (a) requires finding driving force from Newton's second law then calculating power; part (b) involves recognizing that at steady speed, acceleration is zero so driving force equals resistance. Both parts use standard mechanics formulas with no conceptual challenges or multi-step reasoning beyond basic substitution. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(DF - 650 = 1800 \times 0.5\) \([DF = 1550]\) | M1 | Apply Newton's second law, 3 terms |
| \(\frac{P}{20} - 650 = 1800 \times 0.5\) | B1 | |
| Power \(P = 1550 \times 20 = 31000\) W or \(31\) kW | A1 | |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{31000}{v} - 650 = 0\) | M1 | Use \(P = Fv\) with \(F = 650\) |
| \(v = 47.7\) ms\(^{-1}\) | A1 FT | FT on *their* \(P \neq 13000\). Allow \(\frac{620}{13}\) |
| Total: 2 |
**Question 2:**
**Part (a):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $DF - 650 = 1800 \times 0.5$ $[DF = 1550]$ | M1 | Apply Newton's second law, 3 terms |
| $\frac{P}{20} - 650 = 1800 \times 0.5$ | B1 | |
| Power $P = 1550 \times 20 = 31000$ W or $31$ kW | A1 | |
| | **Total: 3** | |
**Part (b):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{31000}{v} - 650 = 0$ | M1 | Use $P = Fv$ with $F = 650$ |
| $v = 47.7$ ms$^{-1}$ | A1 FT | FT on *their* $P \neq 13000$. Allow $\frac{620}{13}$ |
| | **Total: 2** | |2 A car of mass 1800 kg is travelling along a straight horizontal road. The power of the car's engine is constant. There is a constant resistance to motion of 650 N .
\begin{enumerate}[label=(\alph*)]
\item Find the power of the car's engine, given that the car's acceleration is $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ when its speed is $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\item Find the steady speed which the car can maintain with the engine working at this power.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q2 [5]}}