| Exam Board | OCR MEI |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2010 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance with other powers |
| Difficulty | Standard +0.8 This M4 question involves non-standard resistance (power 3/2), requiring separation of variables and integration with fractional powers. While the steps are systematic (F=ma, separate, integrate, apply initial conditions), the algebraic manipulation with v^(-3/2) and the subsequent displacement integral are more demanding than typical A-level mechanics. Further maths mechanics content is inherently harder, and this requires careful handling of non-integer powers throughout. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
2 A particle of mass $m \mathrm {~kg}$ moves horizontally in a straight line with speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at time $t \mathrm {~s}$. The total resistance force on the particle is of magnitude $m k v ^ { \frac { 3 } { 2 } } \mathrm {~N}$ where $k$ is a positive constant. There are no other horizontal forces present. Initially $v = 25$ and the particle is at a point O .\\
(i) Show that $v = 4 \left( k t + \frac { 2 } { 5 } \right) ^ { - 2 }$.\\
(ii) Find the displacement from O of the particle at time $t$.\\
(iii) Describe the motion of the particle as $t$ increases.
Section B (48 marks)\\
\hfill \mbox{\textit{OCR MEI M4 2010 Q2 [12]}}