| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Total distance with direction changes |
| Difficulty | Moderate -0.8 This is a straightforward variable acceleration question requiring only routine differentiation of a polynomial, solving a quadratic equation, and calculating distance with direction changes. All techniques are standard M2 procedures with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step distance calculation in part (iii). |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time |
| Answer | Marks |
|---|---|
| 1 | T = 12 × (0.6–0.4)/0.4 |
| Answer | Marks |
|---|---|
| v = 6 ms −1 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| A1 | [3] | λx |
| Answer | Marks |
|---|---|
| N2L 1 force and RA | 3 |
Question 1:
1 | T = 12 × (0.6–0.4)/0.4
0.1v2
6 = /0.6
v = 6 ms −1 | M1
M1
A1 | [3] | λx
Uses T = /L, (=6)
N2L 1 force and RA | 3A particle moves in a straight line. Its displacement from a fixed point $O$ at time $t$ seconds is $s$ metres, where $s = t^3 - 9t^2 + 24t$.
\begin{enumerate}[label=(\roman*)]
\item Find expressions for the velocity $v$ and acceleration $a$ of the particle at time $t$.
\item Find the values of $t$ for which the particle is at rest.
\item Find the total distance travelled by the particle in the first $6$ seconds.
\end{enumerate}
[8]
\hfill \mbox{\textit{CAIE M2 2013 Q1 [8]}}