| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find acceleration given power |
| Difficulty | Moderate -0.3 This is a straightforward two-part mechanics question applying standard power-force-velocity relationships (P=Fv) and Newton's second law. Part (i) requires simple substitution at constant speed where driving force equals resistance. Part (ii) involves calculating the driving force from reduced power, then applying F=ma with net force. Both parts use routine M1 techniques with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03c Newton's second law: F=ma one dimension6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Driving Force \(= 300\) | B1 | Using \(DF =\) Resistance |
| \(P = 300 \times 40\) | M1 | Using \(P = Fv\) |
| \(P = 12000\) W \(= 12\) kW | A1 | [3] Must give answer in kW |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(P = 0.9 \times 12000 = 10800\) | B1\(\checkmark\) | ft on 12000 |
| \(\frac{10800}{25} - 300 = 1000a\) | M1 | Applying Newton's second law with 3 terms to the car |
| \(a = 132/1000 = 0.132\) ms\(^{-2}\) | A1 | [3] |
## Question 3:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Driving Force $= 300$ | B1 | Using $DF =$ Resistance |
| $P = 300 \times 40$ | M1 | Using $P = Fv$ |
| $P = 12000$ W $= 12$ kW | A1 | [3] Must give answer in kW |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $P = 0.9 \times 12000 = 10800$ | B1$\checkmark$ | ft on 12000 |
| $\frac{10800}{25} - 300 = 1000a$ | M1 | Applying Newton's second law with 3 terms to the car |
| $a = 132/1000 = 0.132$ ms$^{-2}$ | A1 | [3] |
---3 A car of mass 1000 kg is moving along a straight horizontal road against resistances of total magnitude 300 N .\\
(i) Find, in kW , the rate at which the engine of the car is working when the car has a constant speed of $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(ii) Find the acceleration of the car when its speed is $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the engine is working at $90 \%$ of the power found in part (i).
\hfill \mbox{\textit{CAIE M1 2016 Q3 [6]}}