| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | November |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Forces in vector form: kinematics extension |
| Difficulty | Standard +0.3 This is a straightforward application of Newton's second law with vector calculus. Students integrate the force to find velocity (using F=ma), then integrate velocity for position. The calculations are routine with no conceptual challenges—slightly easier than average due to the mechanical nature of the integration and standard kinetic energy formula application. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02f Non-uniform acceleration: using differentiation and integration6.02e Calculate KE and PE: using formulae |
| Answer | Marks |
|---|---|
| (ii) | dv |
| Answer | Marks |
|---|---|
| v= x3 | M1 |
| Answer | Marks |
|---|---|
| [4] | dv |
| Answer | Marks | Guidance |
|---|---|---|
| Page 6 | Mark Scheme | Syllabus |
| Cambridge International A Level – October/November 2014 | 9709 | 51 |
| (iii) | −2 |
| Answer | Marks |
|---|---|
| t = 3 | M1 |
| Answer | Marks |
|---|---|
| [3] | dx |
Question 6:
--- 6 (i)
(ii) ---
6 (i)
(ii) | dv
1/2
0.6v = 0.4v
dx
dv
1/2
3v = 2 AG
dx
1
3∫v2dv =2∫dx
3
3v2
=2x (+c)
3
2
3 2
3 × 12 × = 2 +c
3
2
v= x3 | M1
A1
[2]
M1
A1
M1
A1
[4] | dv
Newton’s 2nd law, a = v
dx
Integrates
Accept omission of +c
Evaluates c (=0)
Page 6 | Mark Scheme | Syllabus | Paper
Cambridge International A Level – October/November 2014 | 9709 | 51
(iii) | −2
∫x3dx=∫dt
8
1
x3
=t
1
3 1
t = 3 | M1
A1
A1
[3] | dx
Integrates using v =
dtA particle of mass $2$ kg moves under the action of a variable force. At time $t$ seconds the force is $(6t - 3)\mathbf{i} + 4\mathbf{j}$ newtons, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors. When $t = 0$, the particle is at rest at the origin.
\begin{enumerate}[label=(\roman*)]
\item Find the velocity of the particle when $t = 4$. [4]
\item Find the kinetic energy of the particle when $t = 4$. [2]
\item Find the distance of the particle from the origin when $t = 2$. [6]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2014 Q6 [12]}}