| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Maximum speed on incline vs horizontal |
| Difficulty | Standard +0.3 This is a standard M2 mechanics question requiring straightforward application of F=ma, P=Fv, and resolving forces on an incline. All parts follow directly from standard formulas with no problem-solving insight needed, making it slightly easier than average for A-level. |
| Spec | 3.03d Newton's second law: 2D vectors3.03v Motion on rough surface: including inclined planes6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
4 A car of mass 700 kg is moving along a horizontal road against a constant resistance to motion of 400 N . At an instant when the car is travelling at $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ its acceleration is $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
(i) Find the driving force of the car at this instant.\\
(ii) Find the power at this instant.
The maximum steady speed of the car on a horizontal road is $35 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(iii) Find the maximum power of the car.
The car now moves at maximum power against the same resistance up a slope of constant angle $\theta ^ { \circ }$ to the horizontal. The maximum steady speed up the slope is $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(iv) Find $\theta$.
\hfill \mbox{\textit{OCR M2 2010 Q4 [10]}}