| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Variable force (position x) - find velocity |
| Difficulty | Standard +0.3 This is a standard variable force mechanics problem requiring application of F=ma with v dv/dx, followed by integration using separation of variables. The setup is straightforward and the techniques are routine for M2 level, though it requires careful handling of signs and understanding that the force opposes motion. Slightly above average due to the calculus integration step, but well within expected M2 competency. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.06a Variable force: dv/dt or v*dv/dx methods |
| Answer | Marks |
|---|---|
| (ii) | dv |
| Answer | Marks |
|---|---|
| x = 3.1(0) | M1 |
| Answer | Marks |
|---|---|
| A1 | 2 |
| 3 | Integrates acceleration |
Question 3:
--- 3 (i)
(ii) ---
3 (i)
(ii) | dv
0.3v =–2x
dx
20
k = – = –62
3 3
20
∫0 ∫x
vdv=− xdx
8 3 0
x = 3.1(0) | M1
A1
M1
M1
A1 | 2
3 | Integrates acceleration
Uses limits or finds constant of
integrationA particle $P$ of mass $0.3\,\text{kg}$ moves in a straight line on a smooth horizontal surface. $P$ passes through a fixed point $O$ of the line with velocity $8\,\text{m s}^{-1}$. A force of magnitude $2x\,\text{N}$ acts on $P$ in the direction $PO$, where $x\,\text{m}$ is the displacement of $P$ from $O$.
\begin{enumerate}[label=(\roman*)]
\item Show that $v\frac{dv}{dx} = kx$ and state the value of the constant $k$. [2]
\item Find the value of $x$ at the instant when $P$ comes to instantaneous rest. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2015 Q3 [5]}}