| Exam Board | CAIE |
|---|---|
| Module | Further Paper 3 (Further Paper 3) |
| Year | 2020 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Acceleration as function of velocity (separation of variables) |
| Difficulty | Challenging +1.2 This is a variable acceleration problem requiring separation of variables and integration. Part (a) involves solving a standard first-order ODE (dv/dt = 3ku - kv) which separates cleanly. Part (b) requires using v dv/dx and integrating again. While it's Further Maths content and requires multiple integration steps, the differential equations are straightforward with no tricks—a competent FM student would recognize this as a standard exercise in their syllabus. The 8 total marks reflect routine application rather than novel problem-solving. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
A particle $P$ is moving along a straight line with acceleration $3ku - kv$ where $v$ is its velocity at time $t$, $u$ is its initial velocity and $k$ is a constant. The velocity and acceleration of $P$ are both in the direction of increasing displacement from the initial position.
\begin{enumerate}[label=(\alph*)]
\item Find the time taken for $P$ to achieve a velocity of $2u$. [3]
\item Find an expression for the displacement of $P$ from its initial position when its velocity is $2u$. [5]
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 3 2020 Q5 [8]}}