| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | March |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Power from work done over time (P = W/t) |
| Difficulty | Moderate -0.3 Part (a) is trivial recall of P=W/t. Part (b) requires P=Fv to find driving force, then F=ma with net force, but this is a standard textbook exercise in mechanics with clear signposting and routine application of two formulas in sequence. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\text{Power} = \frac{750000}{10} = 75000 \text{ W or } 75 \text{ kW}\) | B1 | \(\text{Power} = \frac{\text{WD}}{\text{Time}}\) |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Driving force \(DF = \frac{75000}{25}\) | B1FT | Using \(P = DF \times v\) |
| \([DF - 2400 = 16000a]\) | M1 | Using Newton's 2nd law |
| \(a = 0.0375 \text{ ms}^{-2}\) | A1 | Allow \(a = \dfrac{3}{80}\) |
| [3] |
**Question 1:**
**Part (a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{Power} = \frac{750000}{10} = 75000 \text{ W or } 75 \text{ kW}$ | **B1** | $\text{Power} = \frac{\text{WD}}{\text{Time}}$ |
| | **[1]** | |
**Part (b):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Driving force $DF = \frac{75000}{25}$ | **B1FT** | Using $P = DF \times v$ |
| $[DF - 2400 = 16000a]$ | **M1** | Using Newton's 2nd law |
| $a = 0.0375 \text{ ms}^{-2}$ | **A1** | Allow $a = \dfrac{3}{80}$ |
| | **[3]** | |1 A lorry of mass 16000 kg is travelling along a straight horizontal road. The engine of the lorry is working at constant power. The work done by the driving force in 10 s is 750000 J .
\begin{enumerate}[label=(\alph*)]
\item Find the power of the lorry's engine.
\item There is a constant resistance force acting on the lorry of magnitude 2400 N .
Find the acceleration of the lorry at an instant when its speed is $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q1 [4]}}