| 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 chain rule (v dv/dx = a) and separation of variables. The setup is straightforward, the mathematical techniques are routine for M2 level, and it's a typical textbook exercise with no novel insight required—slightly easier than average due to its mechanical nature. |
| Spec | 6.06a 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 $v\frac{\text{d}v}{\text{d}x} = kx$ 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]}}